BOSTON (AP) — A New York man convicted of killing his ex-girlfriend on Nantucket in 2004 is asking the highest court in Massachusetts to overturn his conviction because two jurors allegedly slept through parts of his trial.

Thomas Toolan III, a former Citigroup executive from New York City, was convicted of murder in the death of Elizabeth Lochtefeld after a jury rejected his insanity defense.

In his appeal, Toolan’s lawyers say two jurors were seen sleeping during the 2007 trial and that prevented Toolan from getting a fair trial.

Prosecutors dismiss the claim, saying the judge saw one juror with his eyes closed briefly, but reminded the jury to pay attention.

The Supreme Judicial Court is scheduled to hear arguments in the case on Friday.

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