Police are investigating the murder of a California couple who were discovered dead in their home next to a disturbing message.

Golam and Shamima Rabbi were each shot at least once in their San Jose property, say police.

ABC 7 reports that a message was written in ink on the hardwood floor beside their bodies saying: "Sorry, my first kill was clumsy."

The couple were discovered on Sunday afternoon by friends who came to check on them.

The friends reportedly entered the home through an unlocked glass door after they had not heard from the Rabbis for days.

The couple emigrated to the US from Bangladesh decades ago. Mr Rabbi, 59, worked as an engineer and Mrs Rabbi, 57, was employed as an accountant.

They were regular attendees of their local mosque, the Evergreen Islamic Center, where worshippers are stunned by the double homicide.

Mosque member Hasan Rahim told the San Jose Mercury: "The loss is so enormous that we are still finding it difficult to come to grips with the truth."

An unnamed relative told the Mercury that police had been questioning one of the couple's two sons - who are aged 17 and 23 - though it is not clear which one.

But police said they had no information yet on a suspect or motive.

Chilling Note Found Next To Murdered Couple