More information would probably be helpful but if I am reading your question correctly, you were driving and stopped at a light when you were hit by a cop on a chase who was without lights or siren. I assume you were injured and want to sue the police officer.
You should get to a lawyer right away. You need to file a notice of claim against the city within 90 days of the accident or you cannot sue.
The issue of the crosswalk notwithstanding, if you are injured, your car being in a crosswalk will reduce but not eliminate the responsibility that the officer had to be careful.
Again, get to a lawyer as fast as you can. You do not have to hire a lawyer from Staten Island but you should get a lawyer who is admitted to practice in NYS.
The consequences of waiting too long to act will be the loss of your legal rights to seek damages to which you may have been entitled to recover.
Check with a lawyer in your locale to discuss more of the details.
You have rights but you must act to protect your rights.
Good luck to you.
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