I think what silver fox is referring to, is the ever-increasing phenomenom of fenced schools. That is a different subject to what I think Ace-digger is aiming at. The fences at schools are not to do with metal detecting, per se. They are due to past litigation about people who go there after school, fall off the monkey bars, and sue the school type stuff. But that said, "fenced" schools usually still have a turn-style type entrance, or propped open pedestrian gate, etc.. And I see people out there after school hours jogging the track, or whatever. So I guess the fences are so that they have a legal out when you slip and fall (ie: "well, the school was closed so tough luck" or whatever).
But barring that, if we restrict your question to parks for example, the answer is no. You do not need permission any more than any other park user needs permission. Ie.: would you need to ask to use the monkey bars? drink from the fountain? etc... But this is a loaded question, because the minute anyone says something like this, someone will come up with a citation of a city, in some state somewhere (VERY few), that does indeed have a "no detecting" rule. If you wonder if the same is true for your city, then look in the books yourself (codes usually available on-line at city web-sites). If there is nothing on the issue, then no, you don't need permission. To think you need permission for a place that has nothing addressing the issue, assumes your hobby is somehow inherently wrong enough, that you had to ask, to begin with. Like, if you were to walk into some city halls, and ask a desk-bound bureacrat, you risk that someone's image will be "geeks with shovels", and then what do you think the answer will be? If you feel you must "ask", then don't phrase it in terms of "permission". Instead, cast the question in terms like this: "Is there anything on the books that prohibits metal detectors in city parks here?" You see how that's different than asking "permission"? Since most cities have never even given the issue thought, there is rarely ever anything addressing it. Thus their answer would have to be "no, nothing addresses md'ing in the books"
Now of course, I would steer clear of obvious historical monuments, even if there was no local ordinances that specifically addressed detecting. And of course, if you're somehow being a nuisance, leaving holes, etc... then someone can take issue with you. But for run-of-the-mill parks, in any city I go to, if I see no signs prohibiting detecting, I consider myself no different than any other park user.