The highest court in Massachusetts is scrutinizing the jury selection process in the trial of a once-prominent doctor who is serving a life sentence in the 1999 killing of his wife.

The Supreme Judicial Court has ordered Judge Paul Chernoff to answer questions about jury selection during the 2001 trial of Dr. Dirk Greineder, an allergist from Wellesley who was convicted of beating his wife, Mabel, with a hammer and slitting her throat.

Greineder's lawyers argue that the jury selection process was closed, violating Greineder's right to a public trial, and are asking for a new trial.

The SJC is asking whether any members of the public were present in the courtroom during questioning of potential jurors and whether Greineder or his lawyer agreed to closed-door proceedings.