At the climax of one of the most closely watched trials in South Carolina history, the packed courtroom was silent except for one woman: the court clerk, who read the guilty verdicts aloud in March 2023 that put Alex Murdaugh, a prominent lawyer, in prison for life for the murder of his wife and son.

Now, a new court hearing is getting underway on Monday to determine whether the clerk, Rebecca Hill, improperly influenced the jurors who voted to convict Mr. Murdaugh, 55, and whether Mr. Murdaugh should have a new trial.

A state police agency is investigating allegations from Mr. Murdaugh’s lawyers that Ms. Hill made comments during the trial that could have influenced the jurors’ votes. Among the allegations are that Ms. Hill told jurors not to be “fooled” by Mr. Murdaugh’s defense, that she had private conversations with a juror, and that she told jurors before they started deliberating that “this shouldn’t take us long.”

Ms. Hill has not been charged, and she has denied many of the most serious allegations. She and the jurors are expected to testify on Monday at a hearing in Columbia, S.C., that is part of Mr. Murdaugh’s appeal of his convictions.

Judge Jean Toal, a former chief justice of the South Carolina Supreme Court, will determine what Ms. Hill did, whether her actions may have altered the outcome of the trial and whether Mr. Murdaugh should get a new trial. It is not yet known whether she will rule from the bench on Monday or issue an opinion later.

The allegations against Ms. Hill, which Mr. Murdaugh’s lawyers first raised in September, are another twist in the tragic tale of the Murdaugh murders, a crime that has horrified and fascinated observers around the country since June 2021, when Mr. Murdaugh’s wife, Maggie, and their younger son, Paul, were shot to death.