It was discovered in the Coolnagard area on Saturday after an incident the night before in which the off-duty officer fired a shot.
A number of homes were evacuated for a time as army bomb squad officers carried out investigations.
Police later confirmed a "crude viable explosive device" was found.
No-one was hurt during the incident on Friday night. Police said an investigation has been launched and the Ombudsman has been informed.
Anyone who witnessed unusual activity in the area over the past number of months is asked to contact Co Tyrone police.
A PSNI statement said: "Police would ask people, especially in the Coolnagard area of Omagh, if they saw anything that gave them cause for concern or they thought out of the ordinary over the past couple of months and specifically between 8pm and midnight on 25 January to contact police.
"Police are also asking if anyone saw anything that raised their concerns in the Kevlin Road area of Omagh during these times, again to contact Police. Police would like to thank local people for their patience and co-operation during this security alert."
Information can be passed on by calling 0845 600 8000.
Meanwhile local politicians have condemned the incident.
Thomas Buchanan of the DUP described it as a worrying time for the PSNI officer, especially as the threat from dissident republican terrorists was severe.
Sinn Féin's Declan McAleer said: "Coolnagard is a very quiet residential area of the town where people from all sections of the community live side by side and where community relations are very good.
"The investigation is still ongoing so I await further details from the PSNI as to the exact nature of the events which unfolded here on Friday night."