A month to month tenant who is otherwise current on rent is entitled under Section 232-b of the Real Property Law to receive one month's notice that you are terminating the lease.
You should consult with an attorney who handles landlord-tenant matters in Ulster County as an eviction proceeding should it come to it, should not be handled pro se.
Answering this question does not create an attorney-client relationship between us. The answer given is for informational purposes only and is not a substitute for contacting an attorney licensed to practice in your jurisdiction and obtaining legal advice from such an attorney.
If you did not ever have a written agreement (lease) with your tenant, then you are guided by principles of common courtesy for the "notice" you use to inform your tenant that you need his cooperation to show his apartment.
If you once had a lease, even though it may be long ago, the notice and access paragraphs from the old lease control you and your tenant in the post lease month to month tenancy.
Without a lease, your ability to show the tenant's apartment, to a great extent will depend on his reciprocal courtesy. If he does not cooperate or he makes an unreasonable demand on you, on your next visit to your attorney, ask what to do, and you will walk out with a thirty day notice terminating the tenancy. Your tenant could decide to cooperate after he is served with a copy of the notice and so matters return to normal, and if he does not see the light, you will be able to go to court when his term ends as per the termination notice and look to evict him.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Before you can show his unit, you must give him a 30 day notice to vacate, if he is current on his rent. If he is not, then you must serve him with a 3-day notice requiring payment before you can evict him. Get an attorney to assit you.