A) What kind of paint is it? Oil based or latex?
B) What kind of a tub is it? Enamel coated steel, acrylic, fiberglass?
If it's latex paint on an enameled steel tub, you'll be able to remove either oil based paint or latex paint with acetone. If it's just a small area, you could probably just use some nail polish remover.
Never ever NEVER use acetone or nail polish remover on an acrylic bathtub because the acetone will dissolve the plastic the tub is made of.