A man in his early 50s and a woman in her late 40s were found with injuries in a Southam street.
The incident took place in Ivy Terrace off Pendicke Street on Thursday at around 2.30pm.
Police had responded to reports of an altercation between a man and a woman and attended the scene along with the ambulance service.
The woman was taken to Warwick Hospital and the man was taken to the University Hospital Coventry.
Police are appealing for any witnesses who may have seen the incident, or can help establish the events leading up to the man and woman being found. If you saw anything, please call 101 and quote incident number 218 of 16 June.
If you want to give information but do not want to give your name you can call the independent charity Crimestoppers on 0800 555 111 or use their anonymous online form at www.crimestoppers.org.uk