If it produces fruit it is female.
Fortunately many persimmon varieties are parthenocarpic - they will produce fruit even when not fertilised but of course the fruit will not have any seeds inside. The fruiting persimmons are all female (obviously) and produce edible fruit without any other persimmon nearby. Those who eat persimmons may have noticed there is rarely seed inside the fruit.
Some trees have both male and female flowers and some male plants occasionally produce perfect (with both male and female parts) flowers and may produce fruit.
You will only need a male pollinator if you want to get seeds.
You should try tasting one of your fruit before opening the fruit market. Some species are not good to eat (some will argue that NO persimmon is good to eat

) The one I have is a species used as rootstock for the fruiting types and tastes terrible even when fully soft ripe.