Officers are investigating an incident after a man reportedly approached two children in a play area.
It happened in Haverhill, off York Road at around 6.50pm on Sunday, June 14.
Police are looking into reports of other suspicious behaviour in the area.
A second incident was reported at around 3.20am on June 17, when a man was seen in a garden on York Road before leaving the area on foot by climbing over garages.
A spokesman for the police in the town said: "I'd like to assure members of the community that I, along with my colleagues in the Sudbury and Haverhill Community Policing Team, take all reports very seriously."
Anyone with information is urged to contact police quoting CAD 36 of June 16.