If your lease has expired, how much notice to move must be given?

Question Details: My lease has expired. We are now tenants at will with no active lease. I have given a 30 day notice to my landlord. They say that I need to give 60 days, as it states in the lease which expired 6 months ago. I have argued that since we are only agreeing for 30 days at a time, a 30 notice is sufficient. Who is right? Is there a statute to support this? Additionally, the landlord states we must fill the oil prior to leaving. It is currently 3/4 full at this. The lease states that we are responsible for paying for propane (thre wrong type of fuel for this residence), but says nothing about refilling the tank.

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