The police vehicles have video cameras. Ask for the video footage. That will clear up what happened. Work with your old insurance company on this. Even though they don't provide current coverage for you anymore, they won't want to pay if they don't have to.
The insurance policy that was in full force and effect at the of the alleged accident should handle the matter. Cooperate with the insurance company on all issues.
Auto insurance is considered occurrence based coverage ( which says the insurance you have in place at the time of the occurrence happens applies) as opposed to claims made coverage (which requires insurance in place at the time a claim is made). Accordingly you must make a claim through the insurance company you had in effect at the time of the occurrence, not your current carrier. Don't delay as doing so may give the former insurer a coverage defense, and reserve rights to defend you or cover any losses. Don't assume because you don't remember or believe you hit the police car, thus will go away, let the old insurer do their contractually obligated job.
LEGAL ADVICE: Unless you have retained me as your attorney, and I am currently engaged by you and providing you with legal advice and services, nothing in this post is intended to be, nor may it be construed as, legal advice.
You should report this claim to the insurance company you had on the date of the crash. Let them handle it. You should cooperate as much as possible with them.
It sounds like the insurance company is saying that your speeding was the proximate cause of the accident. You could fight the speeding ticket. Then, you would understand the cops claim better. If you have full collision, they have to pay anyway. Now you have a new insurance company. Good Luck!
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