Towing Issues: tow said they can request title for my car, storage yards, storage yard

Question
tow company told me as of 30 days they can ask for title to my car


Answer
Yes, No, sometimes...

A key part of this question is missing and that is what state you are in... Each state has different rules and regulations which apply and dictate the procedures.

There is a lien process which tow companies follow in order to dispose of vehicles which are left or abandoned in their storage yard.

Otherwise they would have storage yards full of vehicles which they can not "LEGALLY DISPOSE OF"

I know this is not the answer you are looking for, but it is the best I can do with what I was provided in the question.