A medical examiner on Tuesday said the three kids died by drowning and their deaths were ruled a homicide.
Erin Merdy, 30, remained hospitalized at NYU Langone Hospital Brooklyn on Tuesday. If she is unable to be moved to court, a bedside arraignment is possible.
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Authorities are looking into whether postpartum depression that led to postpartum psychosis could have played a role.
Police say she told her family members she drowned her children but won't speak to investigators.
"So far, she's not said anything," NYPD Chief of Department Kenneth Corey said.
The lifeless bodies of her three kids -- identified as 7-year-old Zachary Merdy, 4-year-old Lilana Merdy, and 3-month-old Oliver Bondarev -- were found on the shoreline of a Coney Island beach after an extensive search.
Police first learned of the children's disappearance early Monday morning, when a concerned family member called saying someone may have harmed them.
When officers arrived at the home on Neptune Avenue, a man who identified himself as the father answered the door and told police he believed the mother was with the children on the boardwalk.
Officers then began to canvas the boardwalk and surrounding area for any sign of the mother or children.
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Ninety minutes later, police got a call from family members who were with Erin Merdy on the boardwalk, about two miles from where the children were found.
"The mother was soaking wet," Corey said. "Whether she had been out in the rain or whether she had been in the water is all speculative at this point. She was wet, she was barefoot, and she was not communicative to the officers."
The search for the children intensified after Erin Merdy was found alone, and police sent in a helicopter and marine units.
The children were found at the water's edge shortly after 4:30 a.m. on a quiet section of beach about 13 blocks from the stadium where the Brooklyn Cyclones minor league baseball team plays.
Efforts to revive them at a nearby hospital failed, Corey said.
Erin Merdy has prior incidents of harassment and aggravated harassment that did not result in charges, but she has no prior arrests or a history of being emotionally disturbed.
Police say the actions appear to be premeditated and not something that occurred at the spur of a moment, and detectives are looking into her past and interviewing neighbors and relatives to determine what had transpired.
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She has not yet been charged.
Eyewitness News also learned that she had been served with an eviction notice, claiming rent had not been paid since sometime last year.
Police are asking anyone who may have seen the mother and children at anytime last night or early this morning to call the NYPD's Crime Stoppers Hotline at 1-800-577-TIPS (8477) or for Spanish, 1-888-57-PISTA (74782).
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