A man and a woman have been arrested on suspicion of assault after leaving a man with head injuries outside St Andrew's Church.
A 20-year-old man and 19-year-old woman, both from Rugby, were arrested after an attack saw the victim, a 22-year-old man from Rugby, treated in hospital.
The incident occurred at around 6am on Saturday, May 12.
Detective constable Steve Mobbs said: "This was a serious assault that has left a man with nasty head injuries.
"We're keen to speak to anyone who witnessed the incident or has any information that could help police with their enquiries."
The man and woman have been released under investigation while enquiries continue.
The woman was also cautioned after being found in possession of cannabis following her arrest.
Anyone with information that could help police with their investigation is asked to call 101.
Alternatively information can be passed on anonymously through independent charity Crimestoppers on 0800 555 111, or by going to www.crimestoppers-uk.org.