Sealand Road was blocked while police and paramedics descended on the address from about 8.45am today (Friday, April 20) but it has since reopened.
The air ambulance helicopter landed on fields at the rear with a woman airlifted to Aintree Hospital in Liverpool. A man, who suffered serious injuries, has been taken to the Countess of Chester Hospital .
Uniformed and plain clothes officers were called to the scene. At its height there were about seven police cars, a rapid response vehicle and two ambulances.
Investigations are ongoing with crime scene investigators now in attendance.
Police are keen to speak to anyone in the area at the time who may have seen something significant which could assist with their enquiries.
Detective Sergeant Stuart Needham said: "Our enquiries are ongoing in a bid to establish exactly what has happened. Officers are in the area speaking to local people but we would specifically like to appeal to anyone who was walking or driving down Sealand Road at the time. This is a busy road and the incident was reported during rush hour.
"We are particularly keen to speak to any drivers who may have dash cam footage at that time."
Officers are currently carrying out house-to-house enquiries, forensic enquiries and CCTV enquiries.
Inspector Barry Brown from Chester Local Policing Unit said: "We would like to reassure the local community that at this stage it is believed to be an isolated incident and enquiries are ongoing.
"Local officers are in the area to provide reassurance and if anyone has any issues or concerns they are encouraged to speak to an officer."
Anyone with information is asked to call Cheshire police on 101 quoting IML 41245, or call Crimestoppers anonymously on 0800 555 111.