Many years (about 40 or so) ago, the family vet we had had at the time (his son took over his father's practice after he passed away) told my mother to be very careful where we walked our dogs (at that time a female chi and a male peke). To not let them sniff and smell where other dogs have gone, pee as well as and especially poop as they can pick up disease(s) by doing so.
Having never forgotten this, I only have mine out in either mine or my daughter's yards. And, because of this, would [I]never[I] even consider going to a dog park. It is always better to be safe than sorry.