Police received a report of a man acting suspiciously around children at a Mosgiel park last month.
The man was reported to have a weapon, however this has not yet been substantiated.
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A police spokesperson said police had identified a person of interest and were following positive lines of enquiry after the incident on Sunday, April 14.
"We understand a report of this nature can cause concern and we urge the community to be alert, but not alarmed."
Police asked the public to report any concerning behaviour on 111 if it is happening now, or on 105 if it is after the fact.
