under NY civil procedure can I move a auto personal injury case to arbitration

There is no way to force a personal injury case into arbitration in NY State. No-fault claims for medical benefits, lost wages and other out-of pocket expenses can be sent to arbitration by one side if you receive a denial of benefits you feel is unjustified. But your claim for past, present and future pain and suffering can only be sent to arbitration if everyone involved in the case consents. You might want to suggest a non-binding mediation instead of an arbitration. There are several independent companies that mediate auto cases in NY - JAMS and NAM being two of the most popoular. Good Luck.

If you are talking about settlement of your personal injuries, you may ask the insurance adjuster to either arbitrate or mediate your case, otherwise, your case should be litigated before a trial judge. If your question involves your no-fault claim, i.e. medical bills or lost wages which have not been paid, the outstanding no-fault claim has to be arbitrated.