Q: If someone hits my car and we both leave where wreck happened can they charge my insurance
A:
NM law requires both parties to stay at the scene of the crash and exchange information--driver's license and insurance. Sounds like you might have exchanged information. Also sounds like no law enforcement showed up to investigate.
Any person can make a claim against your insurance, but the insurance will deny the claim if not your fault. The other person will need to show that you were the cause of the crash. Keep in touch with your insurance company. They would be the best source of information of why they believe or don't believe the crash was your fault.
Tim Akpinar agrees with this answer
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