Although you can't apply oil-based paint over latex because it won't adhere, you can paint latex over oil-based paint as long as you prepare it correctly. To make sure the latex sticks and creates a bond, you'll need to treat the oil-based paint with either sandpaper, trisodium phosphate and a primer, or a shellac sealer.
To test to see if your walls are painted with latex or oil-based paint, perform a denatured alcohol test. Pour a small amount of the alcohol on a clean cloth and gently rub it over the paint. If any paint comes off on the cloth, it's latex. If it doesn't rub off, it's oil-based paint.
If you try to apply latex over oil-based paint without properly preparing it first, the latex won't adhere correctly and will begin to peel over time. For latex to bond with oil-based paint, the surface needs to be dry, dull and clean.
One way to prepare oil-based paint for latex is by sanding it down with a fine, 180- to 220-grit sandpaper to remove its glossy surface. Be sure to protect the flooring underneath as the sanded paint can be messy. Also, old paint applied before 1979 may contain lead. If you think that's the case, call a professional to handle the job. Mix trisodium phosphate with water according to manufacturer's directions. Dip a clean cloth or sponge in the solution and use it to wipe down the sanded surface. Then, clean the walls with plain water and allow them to thoroughly dry before applying an oil-based or latex bonding primer. Finally, apply two coats of latex paint.
Another way to prime oil-based paint for latex is with a shellac sealer, which will adhere firmly to the oil paint. Sand the walls down with a fine-grit sandpaper and then apply the shellac sealer according to manufacturer directions. After the sealer thoroughly dries, which typically takes about one hour, you can apply two coats of latex paint over it. Painting latex over oils can't be done directly -- it will chip off -- but a shellac sealer or primer firmly sticks to the oil paint.