Police were called to an address at Grayswood Crescent just before 7am on Friday and found damage to the window. The caller believed the firearm had been discharged in the early hours.
While they were attending the incident, officers noted that a property in nearby Lymington Drive also had a damaged window.
Subsequent forensic tests confirmed the damage in both cases had been caused by firearms discharges.
No one was injured in the incident.
Three men aged 27, 28 and 31 have been arrested in connection with these incidents.
The 27 and 28 year old men were later bailed pending further enquiries while the 31-year-old man remains in custody.
Det Chief Insp Stuart Spencer of West Yorkshire’s Homicide and Major Enquiries Team, said: “We believe the incident at Grayswood Crescent happened at around 2.30am on Friday and would ask for anyone who saw anything suspicious in the area at that time to come forward.
“We are currently treating these as two incidents as linked, so we would also appeal for any information about recent suspicious activity in the Lymington Drive area.
“We are yet to establish the timing of the incident there, but we believe it to have happened before the damage at the address in Grayswood Crescent.”
Anyone with information is asked to contact the Homicide and Major Enquiry Team on 101, or Crimestoppers on 0800 555111.