Clean it, or have it cleaned, but don't refinish it.
Are you certain that it's a "38 Special"? At that age, it more likely might be made for the .38 S&W cartridge, which is quite different from .38 Special.
Take it around to a few different shops, and ask what each place would do, to clean it and make sure that it's safe to fire.
Beware anybody who says that he would polish or buff any part of it. Antiques should be cleaned, but not polished or buffed.
To get further information, a photo or two would be helpful.