Legal Question in Constitutional Law in New York

You haven't provided much information, but the statements you describe would be hearsay and would probably be inadmissible for that reason. Notarizing them would not eliminate the problem.

The defendant is entitled to cross-examine your witnesses, just as you are entitled to cross-examine his. There is no way to cross-examine a piece of paper, whether it has been notarized or not. That is why hearsay is generally not admissible. (There are many exceptions to the hearsay rule, but the signed statements you have in mind would probably not fit into any of them.)

If you want the court to hear what these people have to say about the defendant, you will probably need to have them testify in court. And if you want to ensure that they will show up, you will probably have to subpoena them.

In addition to what I wrote a moment ago, even live testimony that a defendant "is a violent person" would probably not be admissible. Being a violent person is a character trait. Evidence of a defendant's bad character generally cannot be used to help prove what he did on a specific occasion. The court might allow the testimony if it was admissible for some other reason, but she likely won't let you use evidence of a generally violent character to prove a specific incident of violence.