You have your past and present water bills. You have access to your water meter. Either the numbers match up or they don't - check and see. If the numbers match up and there are no leaks outside of your house, you (somehow) used the water - check, e.g., for running toilets. No joke, I once had a silent leak in a toilet that cost me $300 in a single month.

They certainly can close an account that's in the name of a deceased person, and can make you put the account into your own name to continue service. They can require a deposit from a new customer - and as the account wasn't previously in your name, you are a new customer.