There are two speculated reasons.
One idea is that the two are connected because a leprechaun is a symbol of good luck, and that St. Patrick must have had good luck to finally escape his Irish captors.
Another idea is that in America, all the symbols associated with the Irish people have become one all-Irish holiday with shamrocks, leprechauns, blarney, green beer, and getting drunk at bars just part of the traditions.
Another theory is that the original Irish were indeed leprechauns--which seems the less likely of the three.
Couldn't you just google it yourself?