I don't think there is any state in the U.S. that requires anyone to take a polygraph for any reason.  For certain jobs like law enforcement or intelligence, polygraphs are required to get the job, but you can still decline and just not get hired.  For this legal situation, the police cannot force you to take it.  Just say NO. Do not "try to clear your name."  Let the police dig all that they want without your help.  If you are already a suspect you can't change that, just live with it until you are exonerated. 

Yes, first things first, get a lawyer. 

I would add that you should wait to get a lawyer after you have been served some legal paper work (warrant, arrest, formal charge, summons, etc.).  If you just keep your mouth shut, don't talk to the police at all, decline the polygraph, and the police never take legal action on you and eventually leave you alone, you could save thousands of dollars on lawyer fees that you didn't need.

Sam,

As I mentioned in the chat room, I strongly advise against submitting to any polygraph "test" you may be requested to submit to. The "test" is a fraud that is used by police as a pretext for interrogating a suspect without a lawyer present. Moreover, you'd be wise not to speak with police any further in the absence of legal counsel for reasons that law professor James Duane discusses here:

https://www.youtube.com/watch?v=d-7o9xYp7eE

If police get a warrant to search your computer or phone (or your Internet service provider's records), unless you accessed this site using the Tor Browser or some similar anonymizing technology, they'll be able to determine that you've visited this site. So do see our free book, The Lie Behind the Lie Detector:

https://antipolygraph.org/pubs.shtml

Note that because your "failing" the polygraph can be part of the interrogation plan, polygraph countermeasures are not to be relied upon in this situation.

I fear that there may be a polygraph in my future. Our rental house burned down and I believe my ex was responsible. I was at the home not long before it happened and I saw a car outside when I was leaving. I believe it was my ex. When the neighbors called the police they told us they saw the same car sitting their watching it burn. However, when speaking with the police it seemed more like I was the one they suspected. I know that innocent people get accused of stuff all the time and this would be right up my ex's ally to try and do this right after I had left to make me look guilty. I've had several panic attacks since then, even when I'm home alone. I feel like I will be giving off a ton of false positives and I'm scared. I'm afraid to even download the ebook in case they check my computer or phone. What do I need to do to pass this?