Detectives discovered the device during a follow-up investigation into an incident at a house in the Coolnagard area of Omagh.
No one was injured and, in line with normal protocol, the Police Ombudsman was informed that a weapon was discharged.
A number of homes in the housing development on the outskirts of the Co Tyrone town had to be evacuated during the bomb alert.
Army technical experts spent several hours examining the object and later described it as crude but viable.
Sinn Féin's Declan McAleer said he was deeply concerned.
"I spoke to several of the evacuated residents and they are very concerned that such a sinister incident involving the discharge of a firearm and a suspicious device has taken place in their community. I am therefore relieved that no one has been hurt or injured in this incident” he said.
DUP MLA Thomas Buchanan described it as a worrying time for the PSNI officer especially as the threat from dissident republican terrorists was severe.
A spokeswoman for the PSNI has appealed for anyone who noticed suspicious activity in the Coolnagard area over the past couple of months to come forward.