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You are partially right. The jurisdiction of town courts is unlimited in summary proceedings, but only in regard to back rent due and owing. The Uniform Justice Court Act provides, in relevant part as follows:
§ 204. Summary proceedings.
The court shall have jurisdiction of summary proceedings to recover
possession of real property located in whole or in part within the
municipality, to remove tenants therefrom, and to render judgment for
rent due without regard to amount.
However, counterclaims are not exempt from the regular jurisdictional limit.
While usually a counterclaim against a landlord would be waived if not brought, when a summary proceeding is brought in Justice Court, a party is not precluded from commencing another action arising out of the lease. Real Property Actions and Proceedings law provides as follows:
§ 747. Judgment.
2. The judgment shall not bar an action to recover the possession of
real property. The judgment shall not bar an action, proceeding or
counterclaim, commenced or interposed within sixty days of entry of the
judgment, for affirmative equitable relief which was not sought by
counterclaim in the proceeding because of the limited jurisdiction of
To the extent that a counterclaim is used to set off back rent, however, it can be raised. An example would be if the landlord was supposed to pay utilities, but did not and the tenant had to pay.