I'm not a lawyer, either.
Stephen L. Hoffman states that he is a lawyer, here:
http://www.avvo.com/legal-answers/if-someone-steal-your-car-and-the-is-car-is-not-in-1172002.html
where he wrote:
Most insurance policies will not cover damage caused by a stolen car in some situations. For example, if you left your keys in the ignition with it running (no matter that you need it warm and have a medical reason), I would think most insurance carriers would deny coverage because they would argue you failed to take reasonable steps to secure your vehicle. I'd bet you there is language like that in your policy.
Now, admittedly, Stephen is in Illinois.
Jeff Anderson also states that he is a lawyer (and in NY) on his law firms site, here: http://www.amtinjurylaw.com/auto-accident/stolen-car-1652/
where he wrote:
there are some circumstances where an owner can still be liable for the thief’s negligent conduct. Liability is provided for under New York Vehicle and Traffic Law Section 1210. This section governs an unattended motor vehicle and makes the owner of a motor vehicle liable in certain circumstances.
and
New York courts have found that a violation of New York Vehicle and Traffic law Section 1210(a) can result in liability to the driver or person in charge of the motor vehicle if it is stolen and this section is violated.
Now, admittedly this doesn't directly address whether or not the vehicle which is stolen will be covered by the insurance policy. However, what do you think is going to happen if your vehicle is stolen and the thief kills someone with your vehicle?
Here's a recent article on a local case which should prove interesting to follow: http://www.rochesterfirst.com/news/news-headlines/insurance-company-sued-over-denied-stolen-car-claim