Passing a polygraph won't prove your innocence. Polygraphy has no scientific basis, and the results are not admissible as evidence in Canadian courts. I think the best option for someone in your situation would be to politely decline any offer to take a polygraph test, get a lawyer, and not speak with police without your lawyer present.

With regard to polygraph procedure, you clearly have not understood it. For a "Reader's Digest" explanation, see the AntiPolygraph.org home page and read down the middle of the page (after the list of bullet points):

https://antipolygraph.org

For more in-depth reading, see The Lie Behind the Lie Detector, especially at Chapter 3:

https://antipolygraph.org/lie-behind-the-lie-detector.pdf

When police offer an accused person the "opportunity" to prove his innocence by taking a polygraph test, it's often little more than a pretext for interrogating a person without a lawyer present. The suspect's "failing" may be pre-planned as part of the interrogation strategy. Interrogation techniques can be quite coercive and manipulative. See these lectures by law professor James Duane and police interrogator George Bruch for more on why you shouldn't proceed with the polygraph, or even talk with police without legal counsel by your side. Although they speak specifically with regard to U.S. law, the same general principles are applicable:

Innocent,

Have nothing more to do with the police.  If they want to speak with you, insist your attorney be present.   

If they claim again, that taking a polygraph will exonerate you if you pass it, have them put that in writing, and address it to, you guessed it, your attorney.  And ask them to send a copy to the local prosecutor as a courtesy copy.

TC