If the old paint is peeling, take a good size piece of the peeling paint and hold the edges of it between your thumb and index finger. Exert pressure on both sides of the chip. If it is very flexible and bends easily, it is probably latex. If it is hard, brittle and breaks instead of bending, it is most likely oil-based paint. Another way to test the paint is to wet a rag with denatured alcohol and rub the surface of the paint. If the paint softens or rubs off, it is most likely latex. An alcohol test usually will not affect an oil-base paint.