FMDAC has a section of their website that supposedly answers this .... state-by-state ..... since states vary. But the way they (the FMDAC) got their data, was simply to mail or call each state's park's headquarters, and ask. The problem with that is, you/they might get a "no" or "inquire at each kiosk as you enter", when in fact, prior to the list, a lot of state parks got routinely detected, and no one cared. The reason is simple: in any given state, there is bound to be *some* state parks that are admittedly historically sensitive. And then there are others, that are not historically sensitive in the slightest, or are so big and remote, that perhaps only the cabin at one tiny dot in many square miles is the landmark, but the rest is not cared about. So if you were the person answering such a letter, and had to give a concise answer, you know that it would be nearly impossible to say "well, .... yes at these over here, but no at those 3 over there, or yes on the beach here, but not next to the historic cabin, blah blah blah". So guess what the easy answer is? A lot of them just say "inquire at each kiosk". Well you can guess what happens when everyone starts doing that: Whereas a lot of them probably never gave the matter any thought before, now all of the sudden individual park rangers find themselves answering this question. So what's the easy answer? (they probably envision geeks with shovels). And so on and so on it goes.
California, for example, has some dire sounding rules according to that FMDAC site. But ironically, most of the state parks here are detected with no problem, in full view of anyone and everyone. As long as we stayed clear of obvious historical landmarks, no one ever seemed to care. But in the last 10 or 15 yrs, that climate seemed to change. Some people started getting booted at places where no one ever cared before. All I can figure is, this self-fulfilling prophecy of us thinking we need to ask, thus getting places put off limits. Sometimes we are our own worst enemies.
But to answer your question, it depends. Others will come on here saying "go and ask", thus only continuing the cycle. But it's a catch 22, because how were you/we supposed to know if someone really cared? Another thing you can do is look it up yourself, and NOT ask. Usually the rules are written in a state park's website somewhere. Do a word search on "metal detecting" (or variations thereof). If it is silent on the issue, then go.