My question involves a traffic citation from the state of: Massachusetts

I was going on vacation for 2 weeks, and I felt safe parking my car on a particular street because I had never had a problem parking there in the 5 years I lived there. There are no parking signs on this street, i.e. anyone can park there. I checked the street sweeping schedule and all seemed clear there. But when I got back a week ago, the car was gone. The town's police (Medford) have no record of it being towed, and neither do the towing companies that the police department referred me to. The city's website also says there aren't any outstanding parking tickets. I did find out that there is technically a 48-hour limit for parking in a single spot, which I had certainly broken (assuming my car lasted 2 days in its spot), so there would have been reason to tow my car. But, like I said, the police have no record of the car being towed. I also confirmed with the bank that my car wasn't repossessed. So I filed the stolen vehicle report, and submitted a claim with my insurance company, but I'm still left wondering about the possibility that someone did tow it and failed to alert the police.

So here are my questions:
- Would there be any case where a towing company could tow my car without promptly notifying the police?
- If I did find out that a towing company towed my car without notifying the police, could I take any action against them? What would I be responsible for paying?
- If the error was on the part of the police (e.g. lost paperwork), would I be protected from having to pay a huge bill from the towing company for months of storage?
- Is there anything else I should do in this situation?

Thanks in advance for any advice! It's definitely possible that my car was simply stolen, I just have a hard time believing it based on how safe the neighborhood has been in my experience, and the fact that the car is pretty new with a working security system, though maybe I'm overestimating how secure that is.