* Children found stabbed in luxury upper West Side apartment
* Nanny arrested, in critical condition with self-inflicted wounds
* Mother is a pediatrician, father a CNBC Digital executive (Adds names of victims, details)
By Chris Francescani
NEW YORK, Oct 25 (Reuters) - A mother returned home to her luxury New York City apartment on Thursday to find two of her young children stabbed to death in the bathtub, and the family's nanny was arrested as the suspect in the killings, police said.
The mother discovered the bodies of the little boy and girl at about 5:30 p.m. in their apartment at 57 West 75th Street, near Central Park, on Manhattan's affluent Upper West Side, police said.
New York Police Department spokesman Paul Browne said the children suffered "multiple stab wounds," and were pronounced dead at the scene, he said.
"It's about the worst thing you can hear or imagine," Browne said.
The nanny was lying on the bathroom floor and had stabbed herself in the neck, police said. A bloody kitchen knife lay on the floor nearby, police said.
The 50-year-old nanny, who was not identified, was taken to a nearby hospital and was under arrest, police said.
She was listed in critical but stable condition, police said.
The mother was identified as Marina Krim, 38, police said. The slain children were Leo, 2, and Lulu, 6.
Their father is Kevin Krim, a CNBC executive.
The mother had returned home with a third child, 3-year-old Nessie, after the girl's swimming lesson, Police Commissioner Ray Kelly said at a media briefing.
She saw that the apartment was dark and returned to the lobby to ask the doorman if the nanny and kids had gone out, he said. The doorman said no, and she returned to the apartment to make the grisly discovery, he said.
A neighbor heard the mother's screams and called 911, police said.
A neighbor quoted in The New York Times said she could hear "bloodcurdling screams" from a woman in the apartment.
She said she also could hear the building's superintendent, who had arrived on the scene, yelling: "You slit her throat! You slit her throat!"
The children's father was returning on Thursday from a business trip, police said. Police met him at the airport when he arrived and notified him of the tragedy, police said.
Krim is a senior vice president and general manager of CNBC Digital. He moved to CNBC in March from Bloomberg LLP, where he was global head of Bloomberg Digital. A graduate of Harvard University, Krim was also a former executive at Yahoo.
Neighbors said the children's mother was a pediatrician. (Additional reporting by Jonathan Allen; Editing by Ellen Wulfhorst and Eric Walsh)