An electronic lockbox includes a latching apparatus that uses a rotary actuator with multiple positions to achieve multiple locking states. Multiple positions of the actuator are detected, using optical sensors. The locking mechanism includes an outer sleeve and an inner cylindrical barrel that are coupled with torsion springs. The lockbox has a shackle and a key bin that include latch pins which are retained by the inner barrel when in the locked state, and the barrel can be rotated to either release the shackle or to release the key bin that typically holds a building's key. During insertion of a latch pin into the rotatable barrel, the maximum torque imparted on a first spur gear by the torsion spring, at a maximum rotation angle of the rotatable barrel, is sufficient to rotate the barrel back to its neutral position after the latch pin has been fully inserted into the barrel, and is less than or equal to a back drive torque limit of a prime mover of the rotary actuator.