You have a duty under your policy to cooperate with them. They may want to rule out your involvement in the theft. If you do not give them the info you could lose coverage for the theft.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
Yes, your insurance policy requires you to cooperate in their investigation, so these probably aren't unreasonable things for them to ask for, especially for a large claim like a car theft. If you think they're being unnecessarily instrusive, you can refuse, but they'll likely consider that an unwarranted refusal that voids your coverage.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.