Can I legally withhold rent from landlord for failing to fully fix a leak?

NY Real Property Law 235-b (warranty of habitability) provides that: "In every written or oral lease or rental agreement for residential premises the landlord or lessor shall be deemed to covenant and warrant that the premises so leased or rented and all areas used in connection therewith in common with other tenants or residents are fit for human habitation and for the uses reasonably intended by the parties and that the occupants of such premises shall not be subjected to any conditions which would be dangerous, hazardous or detrimental to their life, health or safety".

Plumbing leaks & flooding conditions have been found by NY courts to be a breach of the warranty of habitability by the landlord. A residential tenant may be awarded damages, if the court finds that the landlord breached the warranty of habitability. Damages for a breach of the warranty of habitability (known as a rent abatement) are determined by a court's finding (calculation) of the difference between the rent under the lease & the rental value during the time the conditions existed in the premises.

If you do not pay the rent, the landlord will most likely start a non-payment proceeding against you in the local town, justice or city court. 

It is important to document the conditions in the premises related to the leak, as well as any expenses incurred as a result of the leak. In addition to documents, you can also include dated photographs & video if the court determines that it satisfies the rules of evidence. If the landlord starts a nonpayment case, you may file a counterclaim seeking an abatement of rent based upon the landlord's breach of the warranty of habitability. After a trial, the court will decide the respective claims raised by the landlord & tenant. Good luck.