My question involves landlord-tenant law in the State of: Connecticut
So I was on a month to month lease and gave 30 days notice and paid for the last month, the month of June. We found a new place and our lease there started June 1. We moved almost all of our things into the new place and got settled on the 6th, thinking we would then go back and clean, take down curtains, AC units, etc. later. The landlord found a new tenant that will start renting either July 1 or June 22nd.
My concern is that I've left some things there and I haven't cleaned at all, and the landlord said she has the right to and wants to start fixing the place up for the next tenant immediately. Which wouldn't be a problem, except she doesn't want to prorate the rent at all for us letting her do that stuff early. My thought was that it's technically ours for the month, and we've had a good relationship so I don't mean to be super penny pinching about it, but I figured it would be a mutual benefit sort of situation, rather than a "thanks for the rent while I get this apartment ready to go for someone else" situation. I'm also concerned that since I haven't given up the keys or done the final walkthrough, any damage or changes made by whoever is in there could be blamed on me.
I looked through some of the laws and can't find anything particular to this situation. Any thoughts?

