Officers were called to Normanton Place in Beeston just after 3pm following reports of a disturbance.
An adult male was seriously injured and taken to hospital fror treatment.
West Yorkshire Police swiftly put a cordon in place before later taping off the M621 exit slip road at junction 2A, as well as the bridge over the motorway at Cemetery Road.
Duty Inspector Tom Harrison confirmed the second scene was connected to the investigation over the incident at Normanton Place.
The cordon around the motorway exit was lifted around teatime although a scene remained in place on the adjacent housing estate.
He said: "The scene is in relation to a call we got just after 3pm today (Sunday). As a result, we are investigating a serious assault involving one adult male victim. His condition is not life threatening.
"Enquiries are ongoing and we are actively seeking a suspect."
Insp Harrison added that officers dealt with an "aggressive dog" at the scene at Normanton Place, although said the animal was not involved in the assault itself.