If your car is still under warranty, by all means take it to a dealer -- preferibly the dealer from whom you bought it, as they will want your return business. They also have certified mechanics and all the necessary diagnostic tools.
If it's out of warranty, and there's a private mechanic you have been able to trust in the past, or who has been recommended, by all means take it to him. There will be a more personal relationship, plus it will be much cheaper if anything serious is wrong.