Bullet casings were found outside the office in the Turf Lodge area on Monday morning.
It is understood that CCTV at the office revealed shots were fired at the office by a gunman on January 3.
West Belfast MP Paul Maskey and MLA Pat Sheehan are to speak to the media about the incident later.
The Police Service of Northern Ireland is investigating the incident.
Detective Sergeant Sam McCallum said officers attended the scene and recovered the casings, which were taken away for further examination.
“We received a report around 11am on Tuesday that bullet casings had been found outside office premises at Monagh Crescent in Ballymurphy the day before,” he said.
“A further report made to us last night (Thursday) stated a number of shots had been fired at the building by a masked gunman on Thursday January 3, just before 2.20am.
“This was a reckless attack in what is a built-up residential area. Someone could easily have been injured, or worse, by a stray bullet.
“Thankfully, we are not looking at any injuries.
“I want to make a number of appeals today.
“Were you in the Monagh Crescent area around 2am and the time the incident occurred last Thursday morning, 3rd December?
“If you own a dashcam, please check your footage as you may have captured footage of the incident.
“Anyone who has information about this incident is asked to call detectives at Musgrave on the non emergency number 101, quoting reference number 367 08/01/19.”