To start off the quest, Mickey needs to talk to Horace at Horace's Detective Agency, the building with the magnifying glass above the door. Horace will tell Mickey about the book he lent to Casey at the Emporium, which is right across the street with the building that has the present over the door.
Once Mickey talks to Casey, he tells Mickey that he finished the book and lent it to Paulie at the Ice Cream Parlor. Mickey must then retrieve the book from Paulie. Once he's done that, he can return to Horace and talk to him to complete the quest.