I don’t know of any specifically, except in fiction.
I don’t know anyone who doesn’t get headaches at all. I do think that sensitive (not necessarily psychic) people may tend to get more headaches. I think headaches tend to correspond to various types of strain. (I expect if I watched PsyDuck from Pokémon for even one hour, I might start to get a headache from trying to watch media I don’t relate to past my tolerance point.)
If you can abstain from going into psychic states, you could try abstaining for say two weeks, count the headaches, then spend two weeks doing psychic stuff and count the headaches. If your interest in the connection exceeds your aversion to the exercise, you could get more and more data on the correlation for you from repeating that sort of experiment. Of course, since headaches and psychic experiences both involve your head & nervous system, it’d be really hard to figure out what the exact cause is – even if they’re highly correlated statistically, you might just have trained yourself to do that. All I see that you could hope to possibly show is that there is not a relationship between them (if that’s the case).
But I do know several people who claim various psychic skills, and the most I hear is that it can be tiring for some people and not others. Some people get headaches when tired. Therefore my guess is some people may get headaches from too much psychic activity, while others don’t.