No, lease agreements do not need to be notarized in New York. Since leases are treated much the same as a standard contract in this state, notarization is not necessary.
As long as the agreement has been reached (and meets the criteria to be legally binding by including signatures from the affected parties), the lease is valid and enforceable. The landlord and tenant can agree to have the lease notarized if they wish, but it is not required.
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The information for this answer was found on our New York Residential Lease Agreement answers.