Are all rental leases governed by state statutes, or must it be stated that the lease is governed by the state?

Our lease states that we must give a 60 day notice to leave our rental. We gave notice on the 7th of the month in writing because for the first week our landlord was out of town (and we had pipes leaking in the basement and they didn't do anything until they came back from vacation!) At any rate, they are stating that we have to pay for the 3rd month of rent because the state statute says that we have to give a notice at the beginning of the month, but, no where in the lease does it say that we are governed by state statutes. Also, we have done nothing to this landlord, we have paid our rent and we are very dissatisfied with the unit and our landlords, they are just doing this to be jerks and I want to know if we can get out of it!?