You can take some denatured alcohol or fingernail polish on a cloth and lightly rub it on an inconspicuous test area.
If the paint softens and is easily removed, then it is a latex paint. If the paint does not really seem to be affected by the test, it is typically an alkyd (oil based) coating.
If you are still not sure, look for an inconspicuous area and with a small tweezer-type tool remove a small chip or sample of the pain. Bring it to Handyman-Hardware and we’ll be glad to tell you which type of paint it is.