By Timothy Mclaughlin

(Reuters) - Two shootings this month targeting police in Indianapolis may be related, police said on Friday, a day after shots again struck law enforcement offices in the Indiana capital.

In both Thursday's shooting and a similar incident on Oct. 4, officers were in the buildings that were hit but none were injured, police said.

According to a police statement, "initial investigative information points to the same suspect (or suspects)" involved in the earlier shooting, which targeted the department's Northwest District Police Headquarters.

The shootings come at a time of intense debate over policing in the United States and use of excessive force against minorities, with numerous cities grappling with how to improve strained relations between law enforcement and citizens.

On Thursday around 11 p.m. local time, officers inside the Indianapolis Metropolitan Police Department's North District Headquarters heard shots and took cover, the statement said.

They did not find a suspect but witnesses heard a vehicle speeding away. Walls and windows sustained damage and a vehicle in the parking lot was also hit, it said.

Sergeant Kendale Adams, spokesman for the department, said on Friday police did not know how many shots were fired or how many hit the building. Adams said police do not have a motive for believe the shooting is linked to the earlier incident.

Police Chief Troy Riggs said multiple rounds hit the building in the first incident and asked the public for help in identifying the shooter.

"An armed attack on police headquarter is an attack on our community. Make no mistake, it is an attack on Indianapolis itself," Indianapolis Mayor Joe Hogsett said at a news conference after the first incident.

(Reporting by Timothy McLaughlin in Chicago; Editing by James Dalgleish)