My car was stolen two weeks ago.  Today I interviewed again witht he deputy sheriff and a detective.  The deputy and I were alone first.  He went through the details of the incident again (even though he had the typed report in front of him).  I assume that was to find any discrepancies on my story.  He then asked if I was willing to polygraph to eliminate me as a suspect since they had no others.  I told him I didn't know much about how they worked or anything but I didn't see a problem.  He said he would go get the list of available dates and times and be right back.
When he came back, he had a detective with him.  The detective sat down and basically said it smells fishy.  He asked lots of questions, but he kept trying to get me to admit to wrong doing.  I had no part of it, and nothing to worry about, so I answered everything as such.  He then mentioned the polygraph again.  Asked if I would take one.  I said I wasn't too sure how accurate they were and he interrupted saying "Oh they are 99.9% accurate!"
He then told me that if I failed, my insurance company likely would not pay out and that they would then pursue charge against me for filing a false report.  I told him I had nothing to worry about.  He did tell me though, that the test was inadmissable in court, and that I could refuse to take it, but if I did refuse, then they would "know I was lying."
He kept after me for about a half hour trying to "give me an out" and admit I was involved.  I stood firm.
When it was all said and done, they never gave me a date or time for the test...just said that if there's anything I want to tell them before the test comes up, they will take it into consideration and "work with me."  I was then told I could leave.

My questions... do you think they were just playing psychological games by offering the polygraph, and I threw a wrench into it?  Also, can the insurance company base their decision on the results of a polygraph or lack of me submitting to one?  Last I knew, it was innocent until proven guilty...and if the polygraph isn't admissible anyway, the burden is on them to find other proof, correct?  And since there is none...the insurance company would seem to have to payout if the car's not found.  They could always go after me at any point later if something came up to show I was involved, and it would only strengthen their case when they add the fact that I accepted their settlement.  Obviously this is not a concern, but it should be their position, right?

Update:

I let them know I was not interested in taking the exam for reasons of time (I work 3 jobs) and the lack of any usefulness of the results.

Earlier this week (note today's date compared to that of my original post) the insurance company notified me that they were satisfied I was not involved and were ready to settle.  One problem:  When the car was stolen I had not yet put the title in my name.  I do a lot of car trading/buying/selling and often I don't register them right away.  This was all covered in the investigation and both the police and insurance company were satisfied I was the rightful owner, but they (insurance) needed the title in my name before they could settle.  I did that back before I even made my first post here.  But since the flag was already in saying it was a stolen car, the DMV wouldn't issue the hard copy of the title until the police had give them the go ahead that *I* was in fact the one who had reported it stolen.  The insurance company when they called eariler this week said they couldn't pay until I had the hard copy of the title.  Since it's been 5 or 6 weeks since I applied for the title and still hadn't received it, it was obvious the police hadn't released it.
I called the deputy sherriff that took the report and had been working on the investigation and left a message (I only ever get voice mail for him) asking if he could release the title sicne the only question holding it up was whether or not I had made the report or the previous owner, and the answer to that was painfully obvious.  I got no return call.  So I repeated my call the next day, still nothing.
Today, I called and asked to speak with his Seargent.  I left a message spelling everything out.  When he called back, he said that there was still a question on the report as to why I would refuse the polygraph.  I explained to him my timeline contraints and told him that I knew the polygraph was 50% accurate at best, and since it couldn't be used in court there was no gain for either of us.  He told me that it was a lie to say it's only 50% accurate and there WAS gain because it would eliminate me as a suspect in a case where they had no evidence, no leads, and no suspects.  He then told me that while there was no doubt that I filed the report they were not going to relase my title until they had exhaust all lines of investigation.

So, to summarize:  They will not release my title, even though there is no question it is my title, until I submit myself to a polygraph which is not admissible as evidence to prove my guilt or innocence.

They know I mde the claim, they know the only question holding up my title is whether or not I made the claim or the previous owner.  And rather than releasing the info as they should they are dangling it like a carrot in front me telling me the only way they will do it is if I take their polygraph.

This seems wrong in my opinion, in more way then one.  I am innocent until proven guilty, and they are holding my property hostage to coerce me into taking the test when they have no leads, and no evidence to indicate I had anything to do with it beyond their lack of any other suspects.

What should I do?  I called a lawyer to setup a consultation regarding this, but will he even be able to help?  It's been 7 weeks since my car went missing, it was a summer driven show car, and here we are halfway through June and I can't try to replace the car so I can enjoy the summer because of them.   

I guess my one other question is, when/if I do go to take the polygrpah afterall, how long does it take for them to get the results processed?  What happens if there is a false positive?  These guys have no other leads as they admitted to me.  Can they continue to string me along?

I am so irritated right now.

The police can leave the case open for as long as they want to in order to pursue whatever leads they have.  If they believe that you are involved in some way, they can continue to investigate you.  They cannot, however, compel you to take a polygraph.  They also should not be holding any paperwork hostage to try to get your cooperation.  It simply isn't good policework.

On the contrary, if I was investigating your case and felt that you were complicit in the theft of your own car, I'd give you the title in a heartbeat.  If you collected your insurance claim and later I discovered proof that you'd been involved somehow that would give me a charge of insurance fraud to add to your false statement charge.  Holding onto the title is a good way to annoy you, but other than that it doesn't further my case at all.

I suggest that since you already spoke with the sergeant you take your complaint up the chain of command.  If you've already hired a competent attorney he should be able to get your title back in no time at all.  They police can only hold onto something like that if it is considered evidence.  If the facts as you stated in your posts are accurate, the title could not be considered evidence.

That's what gets me...if they had ANY leads at all we wouldn't be going through this.  The only reason I'm a suspect is because they have nothing else.  So they are trying to use the polygraph as a psychological tactic to get me to admit to something I didn't do.  I have no doubt that regardless of the answers I give there, they willt ell me I failed to get me to give them soemthing to work with.  And that's not going to happen.  I've got nothing to give them.
I just hate this guilty until proven innocent BS.  Like Sarge said, if they thought they had something, they'd have even more by allowing me to settle this with the insurance company.  The insurance company is satisfied I didn't do it, especially after I showed them the ebay auctions where I had won, paid for, and drove 3 hours each way to pick up, $1100 worth of extras to use on the car THAT SAME WEEK IT WAS STOLEN!
But I think this is straight forward coersion, and I am hoping to talk to a lawyer on monday about it.