Quote Quoting adjusterjack
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There are some statutory limitations on what the landlord can do.

NY RPP Law 235-F - Unlawful restrictions on occupancy.

3. Any lease or rental agreement for residential premises entered into by one tenant shall be construed to permit occupancy by the tenant, immediate family of the tenant, one additional occupant, and dependent children of the occupant provided that the tenant or the tenant's spouse occupies the premises as his primary residence.


So, to some extent the tenant doesn't need the consent of the landlord.

However,

5. The tenant shall inform the landlord of the name of any occupant within thirty days following the commencement of occupancy by such person or within thirty days following a request by the landlord.

http://codes.lp.findlaw.com/nycode/RPP/7/235-f

I'd still like to know what the OP's grounds would be for evicting a rent paying tenant because an occupant got arrested. I don't think housing court would allow for too much creativity.
Oh, I absolutely agree.

New York is just a strange animal at times. This would be one of 'em.