If you had an accident with this person, you can file a claim with their insurance company and if the insurance they shall be investigated and a determination of responsibility. If the insurance is not valid, and they either never have insurance or if the policy has expired or been revoked before the accident, had the insurance company will send a letter rejecting the application on that ground, and you can use this letter, to the uninsured motorist coverage for bodily injury and property damage to please (if you have this coverage).
If you do not know the name of the insurance company and you had an accident, you can go to the DMV and pay a small fee to get verification of insurance for the individual tags.
If you have not had an accident with the person, then you will be able to review their insurance with their permission, since the insurance can not provide verification for you because of privacy laws.