Blamed for car damage I didn't do

What is the name of your state (only U.S. law)? Massachusetts.
I received notification from an insurance company that another car owner whose car was parked next to mine claims that I hit them and did $400 worth of damage to them. I never hit a car while parking, there was no evidence of damage to my car, though my car is commonly parked in the area where they said it happened (near my work), there was no note left for me on my car or anything indicating to me that any accident could have occurred. I think they must have just damaged their own car somehow and picked a random car's license plate to blame. I told them that I couldn't possibly be responsible for it, as I would have noticed if I had hit another car, and left a note for them. Now they're sending the bill to collections! What do I do?What is the name of your state (only U.S. law)?

Report the claim to your insurance company and let them defend you.

Unfortunately, my car is registered in New Hampshire and I don't have insurance (its not required there).

And now you know why you should have it.

so, when the collection agency duns you, send them a dispute and a cease and desist letter. The next step will be up to them.

Also, you will want to keep an eye on your credit report. If this shows up, you will need to dispute it with them as well.