Police spokesman Lt. Roger Keener said a branch office of the NAACP at 1218 B St. was hit by pellet rounds on Aug. 22 and by rocks this past Sunday.
But Davis had different information, saying the office was hit by rocks on both occasions.
No one was inside the building during either incident and no one was hurt, Keener said.
Keener said that on Aug. 22, pellet rounds were also fired into several buildings adjacent to the NAACP office, so there was no indication that the NAACP office was being singled out.
But he said the attack on Sunday "was pretty specific" because the NAACP office was the only building that was hit.
Keener said police are investigating whether the crimes are related and whether they are connected to phone calls that Davis has received from people who "expressed displeasure at their perception of the NAACP's views" on current political issues.
He said that although the callers complained, they didn't make any threats.
Keener said that at this point there's no specific evidence to indicate that the broken windows are hate crimes instead of simple vandalism.
He said police will patrol the area more closely next weekend to try to prevent any recurrences.
Keener said police would like to catch the culprits so they can figure out their motive.
Anyone with information about the incidents is asked to call the Hayward Police Department at (510) 293-7000.