Island County Sheriff's Office spokesman Ed Wallace said an initial investigation found that the woman sustained traumatic blunt force injuries and then was strangled to death. She had been dead for several days when found.
She was identified Sunday as Kathie Ann Baker, 53, of Greenbank.
Wallace said her body was found Saturday at about 10:15 a.m. Saturday wrapped in a tarp behind a home on Silver Cloud Lane in Greenbank that she shared with her husband, 61-year-old Robert Alan Baker.
Robert Baker has been placed under arrest and booked into the Island County jail.
The couple ran a pizza parlor on Whidbey Island, and both worked at the business every day.
Brian Plebanek owns a wine shop next door and said the Bakers seemed happy.
"They were great, everything was fine," he said. "No indication whatsoever (of problems). I'm kind of blown away by this."
Robert Baker is scheduled to make his first court appearance Monday afternoon in Island County Superior Court.