Reports on social media of people trying break-in through back doors of houses around the Banknock area have sparked alarm.
But police officers told worried residents they had only had one report of an attempted break-in.
While they have promised extra patrols to re-assure residents, they have also asked people to report any incidents rather than simply post on social media.
Councillor Jim Blackwood raised the matter with police at Falkirk Council’s external scrutiny committee, and Falkirk Area Commander Damian Armstrong promised to look into it.
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But police officers attending a community council meeting in Banknock on Thursday told residents said there was little they could do to investigate if no-one was reporting problems.
Councillor Paul Garner said the matter had been highlighted to him by Banknock, Haggs and Longcroft Community and he had asked community police to attend the community council meeting.
He said: “The police gave reassurances that the area is being patrolled and also passed on some security advice to those in attendance. I’ve asked them to add this to a hotspot list for additional effort.”