Shoemaker did not represent Bingaman during the trial and said in an interview after the hearing that he doesn't have the jurors' names.
After hearing both sides' arguments, Circuit Judge W. Kennedy Boone III said he would rule on the defense's postconviction motion within a week.
Bingaman was sentenced in January 2008 to 30 years in prison for killing 4-month-old Justice Christopher Calvin Myers-Cannon, who had severe head injuries when he died in January 2007.
Justice was the son of Ashley Myers, Bingaman's former girlfriend.
A jury convicted Bingaman of involuntary manslaughter, first-degree child abuse and second-degree assault. He was found not guilty of first- and second-degree murder.
Justice's relatives have pushed to toughen the state penalty for first-degree child abuse that results in death. Del. Christopher B. Shank, R-Washington, has sponsored a bill to increase the maximum sentence from 30 years to life in prison, but the bill failed this year and last.
Several relatives were in circuit court for Monday's hearing. Bingaman did not appear.
Asked by Boone if the request was based on suspected jury misconduct or a general concern, Shoemaker said, "It's a bit of a hybrid of both of those."
Shoemaker said he didn't intend to contact jurors as part of the research, but he wants to check for possible misstatements they made when they were impaneled.
Michael noted that a change last year in Maryland's criminal procedure rules required the jury list be returned to the court.
That directive was not in effect in 2007 when Bingaman was tried.
Michael said he doesn't know how a juror's lie could be proven because a juror can't testify during a postconviction hearing.