No doubt you will find folks who say to ask permission, from every desk in city hall you can find. But go figure: you're asking on a forum where some folks say you need permission to hunt sandboxes in any park anywhere. So go figure, you're going to get the gammut of answers.
If it were me, I'd check for myself at the city's website, to see if there's any specific rules forbidding detecting. Most all city's now have websites. And the city codes, laws, etc... are usually a link there. Maybe even specifically for the park's dept. subsection, where they'll list rules for the parks (no alcahol, dogs on leash, etc...). If you see no prohibitions for metal detectors .... well then .... I guess it must not be prohibited. If the city doesn't have a website, then the laws are usually available for public viewing at the desk (as publically available info) at city hall.
This is preferable to going in and asking a live person, because you risk someone's opinion (ie.: they morph something else to apply to your question, when .... truth be told, they might never have noticed or cared or given the matter thought before).
But others here, upon hearing the word "historic", will tell you you can't, or you need to grovel, etc.... If there's no specific rules saying "no detecting", I'd do it. Naturally be discreet (ie.: go at low traffic times, don't go during the middle of an archie convention, don't be in the middle of retreivals when busy-bodies are watching, etc....)