All evidence should be given to your lawyer. If the lawyer thinks it is wise to give something to the police, they will advise as much. If you are involved in a fight with a white person, then it'll be your word versus the word of the white person, and the cops will want to side with the white person. The evidence you provide which you might think is "on your side" might very well still be used against you.

When dealing with cops, lawyer up. Even if you can't afford it. It is better to be indebted to a law firm than to risk a death penalty.

EDIT: typo fixed