A suspicious fire broke at a block of flats in the Portlec Place area of the town.
At approximately 8.45pm on Friday, 24 July police received the report.
Due to the amount of smoke a woman was taken from the building by NIFRS personnel.
It is not believed she suffered any injuries and the small fire caused minor damage.
Detective Sergeant Bell said: “I would appeal to anyone who has any information or witnessed any suspicious activity in and around these flats yesterday evening to contact detectives at Lurgan on the non-emergency number 101, quoting reference 1866 24/07/20.
“Anyone with any information about this incident or who may be able to help with our investigation, is asked to call us on the non-emergency number 101, or submit a report online using our non-emergency reporting form via http://www.psni.police.uk/makeareport/. You can also contact Crimestoppers anonymously on 0800 555 111 or online at http://crimestoppers-uk.org.”
Earlier this morning, Upper Bann DUP MP Carla Lockhart described it as a “terrible ordeal” for those directly affected.
“I know all of the residents living in these flats and their families and this has been deeply traumatising,” she said.
“It is no doubt a shock to have their Friday evening disrupted in this way and I would wholeheartedly condemn those who did this. If anyone has any information please come forward to the PSNI on the 101 number.
“I want to pay tribute to the emergency services for how swiftly and professionally they dealt with this matter, before it could become a more serious incident.”