As I recall in Florida, LL doesn't have to give even that: 15 days in your state.
See Florida statute : 83.57 Termination of tenancy without specific term.--A tenancy without a specific duration, as defined in s. 83.46(2) or (3), may be terminated by either party giving written notice in the manner provided in s. 83.56(4), as follows:
(1) When the tenancy is from year to year, by giving not less than 60 days' notice prior to the end of any annual period;
(2) When the tenancy is from quarter to quarter, by giving not less than 30 days' notice prior to the end of any quarterly period;
(3) When the tenancy is from month to month, by giving not less than 15 days' notice prior to the end of any monthly period; and
If your lease requires 30 days notice then you are probably obligated to pay for March also.
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If you are month-to-month, then the Landlord can give you a fifteen day notice prior to when rent is due and you must be out by the beginning of the next period. For example, if rent is due on the 15th of the month, the landlord has to give a notice by the last day of the previous month and then you must be out the end of the day the 15th.
Was the 60 day notice period for non renewal of the lease? or was it for early termination of the lease? Either way, the 60 day notice would only apply if there was specific language that the 60 day notice would apply to a month-to-month lease after the original lease expired.
Although Florida Statutes only require a landlord to give not less than 15 days notice of termination prior to the end of the monthly period, that may not apply where there was originally a written lease. Material provisions of the lease survive expiration of the lease where the tenant remains in possession with the consent of the landlord. For example, the amount of rent to be paid. Just because a lease expires and the tenancy becomes month-to-month does not mean that the all of the lease terms expire and the parties revert to the Florida Residential Landlord and Tenant Act. You should consult a landlord-tenant attorney on your particular facts.
Disclaimer: Please note that this answer does not constitute legal advice, it is for informational purposes only, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.