What the other answers failed to mention is that static electricity shocks have a very high voltage measured in thousands of volts. The 12V voltage of a car battery is way too small to cause any buildup of static electricity.
The high voltage of static electricity shocks is so high that if the voltage was continuous, it the current would kill you. The reason static electricity shocks don't kill you is that there is a limited amount of charge, and when the charge is depleted, the current flow stops.
So, the answer to your question is that your car battery has absolutely no possibility of causing static electricity shocks. To verify this is true, do this simple experiment: touch the negative terminal with your left hand and the positive terminal with your right hand. Do you feel a static electricity shock? If not, there is no way the origin of the static electricity could be the battery.
Edit: I should mention that in theory somebody could build a device that up-converts the low voltage of car battery to a voltage high enough to cause static electricity shocks. So, in theory, with a suitable device you could use the low 12V voltage of a car battery to create static electricity. Does your car have such a device? Probably not, unless you have added such a device to your car.