A Minnesota elementary school teacher and his husband who were both being investigated in a criminal case have been found dead in an apparent murder-suicide on an island in Washington state.

Aric Babbitt, 40, and Matthew Deyo, 36, of South St Paul, were found dead of gunshot wounds on a Lopez island beach Thursday, according to San Juan County Sheriff Ron Krebs.

Babbitt, who taught at Lincoln Elementary School in South St Paul, was under an investigation along with his spouse for allegations that authorities declined to specify, citing an active investigation.

Mystery deaths: Minnesota teacher Aric Babbitt, 40 (pictured), and his husband, Matthew Deyo, 36, were found dead in a murder-suicide in Washington state Thursday

A kayaker came upon the body of one of the spouses on a Lopez Island beach (pictured)

The South St Paul School District placed Babbitt on administrative leave two weeks ago after learning of the allegations against him and launched its own probe.

South St Paul Police chief Bill Messerich revealed that detectives have executed a search warrant at the home of Babbitt and Deyo, and called the case involving the couple 'a tough one'.

In hot water: Babbitt, pictured here with his niece, was under a criminal investigation along with his spouse

The Daily Mail on Tuesday reached out to the South St Paul Police Department for comment about the case and is awaiting a response.

Babbitt's sister, Sara Babbitt, revealed in a text message sent to a friend, and later forwarded to the TwinCities Pioneer Press, that her brother and his husband 'felt like they didn’t have an out and ending their lives was the best for them'.

Ms Babbitt also said that on Thursday, the day the couple were found dead in Washington state, she received a letter in the mail from Babbitt.

Sheriff Krebs said in a statement that a kayaker came upon the body of one of the spouses on a Lopez Island beach Thursday.

Police officers who were called to the scene later discovered a second body.

Both died of gunshot wounds, and the incident was ultimately ruled a murder-suicide.

Witnesses on the island reported hearing the sounds of gunshots at around 8.30pm Wednesday.

Veteran educator: Babbitt had taught at Lincoln Elementary School (pictured) in South St Paul, Minnesota, for 14 years

No way out: Babbitt's sister revealed in a text message to a friend that her brother and his husband 'felt like they didn’t have an out and ending their lives was the best for them'

Police have executed a search warrant at the couple's home in South St Paul (pictured)

A suicide note was found at the scene of the crime, which stated that the couple had visited Lopez Island years ago with their dog and loved it.

Babbitt had worked at Lincoln Elementary School for 14 years, teaching first, second, fifth and sixth grades. He was set to teach fourth grade beginning next month.

The 40-year-old teacher had no history of disciplinary actions at his workplace, according to the school district.