If a vehicle is towed, am I allowed to get my birth certificate and credit cards out of the vehicle?

More information is needed. Who impounded or towed the car?  Is there a fine to pay in order to get the vehicle?    In general, the quicker that you pay, the less that you may have to pay. At a certain point, your car may be sold or scrapped for metal.  Usually, but not always, the contents of the vehicle are not accessible.  You will have to check with the party or government entity that has possession of the car to see whether it will return personal documents.