The pair have been named locally as Jim Quigley, 69, and his wife Marie, 70, from near Hackballscross, County Louth.
He died when his car hit a truck and another car on the M1 on Monday.
When police called to the registered address of his car, his wife's body was found in a upstairs bedroom.
It is believed Mrs Quigley sustained serious head injuries.
Irish broadcaster RTÃ‰ reported on Tuesday that police are treating her death as murder and "keeping an open mind in terms of covering all aspects of the investigation".
She was found dead at about 15:45 local time when police, accompanied by the couple's son, went to notify the family of Mr Quigley's death.
The crash happened earlier near Ardee, County Louth, at about 14:00 local time.
It is reported that Mr Quigley veered into the path of the lorry on the northbound carriage of the M1.
Three people sustained injuries that are not believed to be life-threatening.
On Tuesday evening, the couple's relatives issued a joint statement appealing for privacy and time to grieve.
"We would like to thank our extended family and friends for their continued thoughts and prayers," the statement said.
Police investigating a married couple's deaths in the Republic of Ireland are treating the woman's death as murder and investigating the possibility that she was the victim of a murder-suicide.