A town road was closed off after armed police were called in following reports a woman had been attacked before a man fled with a knife.
Officers were seen in Murston Road, Sittingbourne, at about 5.40pm yesterday.
It is understood the road, off the A2 and one of the main routes to Murston, was shut.
A police spokesman said: "Kent Police was called at 5.43pm on Tuesday, December 14 to a disturbance at a private address in Murston Road, Sittingbourne.
"A man is reported to have assaulted a woman at the property and no medical treatment was needed.
"It was also alleged the man had threatened to harm police officers if they attended, before leaving the address in possession of a knife.
"Officers, including armed officers, attended the scene and conducted a search of the area.
"At present, no arrests have been made and enquiries to locate the suspect are ongoing."