A Connecticut man has pleaded not guilty to killing his wife, who was reported missing in 1984 but whose bones were discovered in 2010 under the floor of a barn that was being renovated.

John Heath, 68, of Bridgewater, Conn., was arrested on Monday and charged with murdering his wife Elizabeth Heath, 32 at the time of her disappearance.

"On April 6, 1984, John Heath arrived at the Newtown Police Headquarters to report his wife Elizabeth Heath as missing," police said in a statement.  "According to Heath's statement at the time, Elizabeth had left in the middle of the night on either April 1 or April 2, 1984."

Police said the motive behind the killing was that Heath did not want to have any more children after the couple had one daughter, according to ABC News' New Haven affiliate WTNH. The couple were getting a divorce at the time of Heath's disappearance.

Elizabeth Heath was listed as a missing person with an unsolved case for 26 years until her body was found in April 2010.  Her remains were discovered under the floorboards of a dairy barn that had previously been owned by John Heath, according to police. The new owners were renovating the barn when they found the skeletal remains.

The body was identified as Elizabeth Heath's and her death was declared a homicide, police said. An autopsy showed that she had died from blunt force trauma to the head.

Since the discovery, authorities have been "involved in an exhaustive two-year investigation which culminated in the arrest of John Heath," according to the statement.

(Image credit: Newton Police Department)

Newtown Police said there was not a specific piece of evidence that led to Heath's arrest, but, rather a series of circumstances that supported the charge, according to WTNH.

"He has said nothing to implicate himself in this crime," Police Chief Michael Kehoe said at a news conference.

Heath's current wife Raquel Heath covered her head with a hood as she left court on Tuesday and angrily shouted, "No comment" at reporters.

State Attorney Stephen Sedensky told ABCNews.com he "can't comment on a pending case." The public defender's office did not respond to request for comment.

Heath was arraigned on Tuesday and is being held on a $1 million bond. The judge scheduled Heath's probable cause hearing for June 19.