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8:30 AM PT -- Law enforcement sources tell us ... cops are NOT planning on conducting a criminal investigation into the death at this point ... and believe there was no foul play.

We're told a post-mortem examination (autopsy) is currently being scheduled and is expected to be conducted in the next few days.

Meanwhile, Kate and William's rep has issued a statement on behalf of the royals saying they are "deeply saddened" by the news ... adding, "Their thoughts and prayers are with Jacintha Saldanha’s family, friends and colleagues at this very sad time."

A nurse at the hospital where Kate Middleton was treated for morning sickness this week has been found dead ... and suicide is suspected -- after she mistakenly transferred a prank radio call to Kate's hospital room.

According to law enforcement, the woman was found dead at an address near King Edward VII hospital, where she worked, around 9:30 AM this morning.

Paramedics were dispatched to the scene but were unable to revive her. Scotland Yard is treating the death as a possible suicide.

The woman -- a nurse identified as Jacintha Saldanha -- was the victim of a prank by an Australian radio station, which called King Edward VII hospital on Wednesday pretending to be the Queen of England (with a terrible accent) and asking to speak to Kate.

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The nurse immediately transferred the call to Kate's room, where another nurse then nervously explained Kate's condition over the phone. The call was broadcast all over the planet.

The radio station issued an apology just hours after the prank aired, saying, "We were very surprised that our call was put through. We thought we'd be hung up on as soon as they heard our terrible accents. We’re very sorry if we’ve caused any issues and we’re glad to hear that Kate is doing well."