If you have a standalone FAA PPL you need the appropriate FAA medical. (CFR 61.3 (c)(1))
If you have a "piggyback" FAA PPL (based on an EASA/JAR PPL and issued as per CFR 61.75) you can use your JAA/EASA medical or an FAA medical - your choice. (CFR 61.75 (4))
But if you have a UK issued JAR-FCL or EASA-FCL licence and medical, and you limit your N-reg flying to the country that issued it (the UK in this example), you don't even need an FAA PPL or medical at all. Your UK issued licence and medical will suffice. (CFR 61.3 (a)(1) and 61.3 (c)(2)(x))
eCFR ? Code of Federal Regulations