In New York, the answer is “Yes”.
In New York State, being partly to blame for an accident doesn’t prevent you from filing a claim for your injuries, or collecting compensation for them. While each case is different from any other, if you are partially at fault the court will generally reduce your maximum possible award by the percentage of your fault. That is, if the severity of your injuries is determined to deserve an award of $1,000,000 and you are 30% at fault, your award will be reduced by 30%, or $300,000. Your net award will be $700,000.
Of course, the possibility that you are partially at fault introduces yet another complicating factor to your claim. This is another solid reason why you should hire a Personal Injury attorney at the earliest possible moment, and rely on her for advice every step of the way.