Is there any performance problem if a static array is returned from a method?

Why would you want to return a static array from a non-static method?
It's probably a bad idea: a static array will have only a single instance app-wide, and a non-static class can have multiple instances - and with modern OSes, multithreading means that the app could be processing on several different instance at the same (or similar) time.

So if your method fills and returns a static array, and a second instance does the same with different data, then both of them will be working with the last set - the previous one will be discarded. This will happen even if your aren't multithreading: if one instance saves a copy of the returned array for later use and the same method is called on a different instance, the first will still lose it's "original" data.

I'd say on balance there would need to be a very, very good reason for doing that - the scope for some awesomely difficult-to-fix bugs happening later when you've forgotten about this are far, far too great.