The current law in Germany divides between
Exhibitionism (§183 Abs. 1): Only applicable to men (!), there was in fact a constituitional complaint which was rejected by the highest court in Germany. The targeted person needs to feel bothered and the exhibitionist must display a sexual pose (erection, sudden exposure, display before minors). Punishable with 1 year prison or hefty fine, the person must be also diagnosed by a expert witness. Probability: nil.
Erregung öffentlichen Ärgernisses (§183a, public indecency): Everything with sexual content which is not exhibitionism, also applicable to women. Also punishable with 1 year or hefty fine. Probability: very low, the problem is how you define "sexual behavior". A verdict of the highest court in Bavaria excludes especially pure nakedness from public indecency.
Störung der Allgemeinheit (§118, Disorderly conduct). This will be the law which will be encountered at the worst case. Fine between 5 - 1000 €, most likely something between 30-100 €.
Now to the specifics and local customs.
Naked sunbathing at the beach is accepted. Either there are signs explicitly forbidding it or FKK beaches where you must be naked.
Sunbathing in the park is a gray zone. Some parks like the Englische Garten (English garden) in Munich, nearly all parks in Berlin (Charlottenburg, Tiergarten etc.) are used by nudists. That there are some zones in some parks is simply because you want to be with other people, everyone knows what to expect and you have no problems if some idiot starts to complain.
If you choosing a place which is far away (30 m) from the paths or you see other naked people, I do not see a problem with naked sunbathing in a park. If you are very unlucky, some lockjaw turns up and complains or call the police. Because the police is bugged with these kind of complaints, they will normally turn up, give you the wiggled finger ("Please do not do this again and leave the park") and leave. Do not resist and search another park. If on the other case they do not turn up, this is a clear sign.