It's risky, but you might try going to the clerk's office at the court where the case would be. The court clerk's office usually is not equipped to take people into custody, and it seems safer than going to the police station. If it's a traffic or misdemeanor case and you know an attorney, see if he/she will help you pro bono by going to the clerk's office on a day that they're already going to be at the courthouse to make the inquiry for you.
The only way to find out if you have a warrant is to ask the clerk at the police department to check and see if you have a warrant. However, this may get you arrested if they do find that you have one. For more details, check http://www.ehow.com/how_4794929_check-warrant.html.