is such thing as verbal lease

By tony

Me and my gf moved into an apartment in NH. We did sign a lease for six months. Some things happened and we split up, i moved out and one of her friends took my place in the apartment.
I know that when i moved out and she moved someone else in place of me that the original lease becomes void.
The landlord did not have them sign a new lease. When i last talked to her she said they had a month to month verbal lease.
My ex moved out on the first of Feb, and the landlord is refusing to return the deposit because she is saying that she broke the lease for reasons we cant figure out.

Another reason she is refusing to return the deposit is because of a heating issue. we signed a lease saying we would use only 500$ in propane the entire time we were there.
Around Nov. the heat stopped working, we contacted the LL , she told us to turn the heat up all the way and give it awhile and that should fix the issue. We gave it the rest of the day. Still nothing, so we talked to her again. she told us that she had scheduled an appointment to have it looked at, not telling us when it was for. a week went by and still nothing so we contacted her again. she contacted them "again" and the next day they came and fixed it. Also saying that it needed to be fully maintanenced, along with the note the repair man gave her i also told her what he had told me about it needing maintanence.
We had the heat on for about two weeks later, mind you the house still wasnt above fifty degrees, and then the heat went out again. this time it was only a few days till she had gotten someone in, due to not being able to get ahold of her.
but it was enough time for the heat to drop again. and again it took about two or more weeks to get the appartment back to a comfortable temp.
The issue is that she is saying that it is our fault that we used  more than our 500$ alloted for heat.
Is this really our fault.?

and should we be able to get our deposit back.?

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Holy Cow, we couldn't find any other related post. Sorry. :(