The accusation came up as Zimmerman's lawyer argued to have Martin's parents banned from the courtroom since Zimmerman's parents were not allowed to be present for the proceedings. If the judge declined to order Martin's parents out, the lawyer asked that both sets of parents be allowed be present.
The dispute arose during the first day of the trial in which Zimmerman, 29, is charged with the murder of Martin, who was 17 when he was killed in February 2012.
Before the trial started, Judge Debra Nelson ordered Zimmerman's family to leave the courtroom because they are on the prosecution's list of possible witnesses and witnesses are barred from the court until they testify.
Martin's parents were allowed to stay because Florida law allows the immediate family of victims to remain in court.
Defense attorney Mark O'Mara asked that the judge allow Zimmerman's parents to also be present. The lawyer said he was seeking "an appropriate setting," and said it was "lopsided in favor of the state."
In making his argument, O'Mara told the judge -- the jury was out of the room at the time -- that Martin's father Tracy Martin had "threatened or cursed at one of my client's family members."
Tracy Martin could be seen shaking his head at the suggestion.
The judge said that she had observed the court audience and found that, "everybody has been very well behaved," so the incident, "if that happened, it happened during recess."
O'Mara called witness Tim Tuchalski to the stand who said that two weeks ago that while he was entering the courtroom wearing a tag identifying him as member of the Zimmerman family Tracy Martin swore at him while passing him.
"He seen me and seen my badge and said motherf***er under his breath," Tuchalski told the court.
He said, "I was holdling the door for him and his wife."
Under questioning by prosecutor Bernardo de la Rionda, Tuchalski said, "That's what I believe I heard." When pressed by de la Rionda, he added, "I'm sure that's what I heard."
He said the incident happened two weeks ago and at the time told Zimmerman's wife Shellie Zimmerman and later told court deputies.
When asked why he was testifying about it two weeks later, Tuchalski said, "I didn't want to make any ripples… I didn't want to make anyone sound bad."
The questioning did not change the judge's mind. She ruled that Martin's parents can stay in the courtroom and Zimmerman's must stay out because they are on a list of witnesses.