Is it considered a month to month tenancy if we did not sign the lease after it expires?

Yes, all leases convert to month-to-month tenancies if no new lease is entered into, however the terms of the expired lease still apply. So if your old lease required 60-days' notice, then as a month-to-month tenant you must still give the landlord 2 months' notice to terminate.

Agree. Two other things though... If your old lease was silent on how much notice you need to have given, then you are only required to give 30 days notice on a month to month. Also, you stated you "did not sign the lease after it expires". If the landlord offered you a new lease, and you didn't sign it, the landlord could try and treat you as a holdover tenant, which could subject you to double rent.

Attorneys Rothbort and Wurms are both correct but you only say you "were told" there's a 60 day notice. Check the underlying (expired) lease to be sure the landlord is not lying or mistaken.