Edward Furneaux, 74, died after crashing his car into a tree in Kewstoke Road, Worle, on the morning of 19 January.
The body of his 70-year-old wife, Anne, was found at a property in Pilgrim's Way the same day.
No-one else is being sought in the murder inquiry into Mrs Furneaux's death, Avon and Somerset Police said.
A husband and wife who died in an apparent murder-suicide in North Somerset have been named.