Officers arrested a 30-year-old man who was found with a replica firearm.
A Cumbria police statement said: “At approximately 3.20am, Saturday 12th October, the Police were called to a construction site near the Northside Road area of Workington in response to a call from a member of the public reporting that a man was being threatened by a man with a gun, he was uninjured.
“Shots were believed to have been heard and following this, the suspect ran from the scene. A number of Police Officers quickly attended the area, which included support from armed officers and a dog handler.”