In a small bowl, combine the flour, baking powder, baking soda and salt. In a large bowl with a mixer at medium speed, beat together the butter and peanut butter until well blended. Add the sugars and beat until well blended. Beat in the egg, orange rind and vanilla; then add the flour mixture and beat well. Cover and refrigerate for 1 hour.
Shape the dough into 1-inch balls and place on an ungreased cookie sheet 2 inches apart. Flatten them with a lightly sugared fork, making a crisscross pattern
Bake in a preheated 350-degree oven for about 12 minutes or until lightly browned. If desired, score with a skewer after 5 minutes of baking. Cool on a wire rack.