If a property or site manager makes such allegations, then you can certainly contest the allegations. If they are false, you should submit to the Court that they are false. However, calling them hearsay is incorrect, and you should not label them as such unless they actually ARE hearsay.
Hearsay is an out-of-court statement offered to prove the matter asserted in the statement. In cases where a party might feel threatened or intimidated by the person opposing the hearsay statement, the Courts will seldom force that person to take the stand to testify and be subject to cross examination. However, the offering of documentary evidence, such as police reports, etc. is normally an acceptable alternative. The fact of the matter, however, is that the Housing Court is extremely busy, and they don't like to waste time on things that probably won't affect the outcome of the case.
Since you are confronted with statements that you allege to be false, and you already appear to be involved in eviction proceedings, it is time to hire an attorney, or find a pro-bono attorney. If you already have one, you should be having this conversation with them.
This does not constitute legal advice or the engagement of my services as an attorney.
Dear New York Tenant:
Testimony in a trial by a witness with claimed personal knowledge is considered direct testimony. It is not hearsay. A trial judge makes a decision based upon the admissible evidence including oral testimony. The judge is allowed to factor into the weight of any oral evidence the lack of a contemporaneous paper trail recording the alleged incidents. The landlord may have video evidence of the incidents. There may be records of reports to the police.
This is a serious matter and the tenant should consider hiring an attorney to assist in protecting the tenancy.
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.