The only direct experimental result on antimatter and gravity comes from Supernova 1987A. This supernova in the Large Magellanic Cloud emitted both neutrinos and antineutrinos, some of which were eventually detected on Earth. Those neutrinos and antineutrinos took 160,000 years to reach Earth, and while travelling were bent from a "straight line" path by the gravity from our own galaxy. The bending with gravity changed the time needed to reach Earth by about 5 months, yet both the neutrinos and the antineutrinos reached Earth at roughly the same time (within the same 12 second interval). This shows that the neutrinos and antineutrinos "fell" similarly, to a very high level of precision (about 1 part in a million). [4] and [5] provide some background information on this.
However, this does not necessarily tell us that matter and antimatter will fall similarly to the same level of precision when dropped on the Earth, because they could be affected differently be some new, unknown force which has too short a range to be seen on galactic length scales.