NEW YORK (CBSNewYork) — Jury selection began Monday in the trial of an Upper West Side nanny accused of murdering two young children in her care.

Yoselyn Ortega, 55, is charged with two counts each of first-degree and second-degree murder for fatally stabbing 6-year-old Lucia Krim and her 2-year-old brother Leo on Oct. 25, 2012.

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Potential jurors are filling out questionnaires about the case.

The notoriety of the case could pose a challenge. It could take as long as two weeks or more to find an impartial jury, WCBS 880’s Peter Haskell reported.

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The children were found in a bathtub by their mother when she returned home to the family’s luxury apartment building at 75th and Columbus Avenue. Each had been stabbed multiple times with a kitchen knife, police said.

Ortega had stabbed herself in the neck before police arrived. She was hospitalized for weeks.

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The court found her mentally fit to stand trial but her defense will try to raise doubts.