John Alcorn, of Bristol, Conn., arrived at Suffolk Superior Court shortly after 9 a.m., accompanied by his attorney, Matthew Dyer. Dyer declined to comment as he entered the building with his client.
Alcorn, 21, is related to Thaddeus Singleton III, the deceased husband of Tanya Singleton, a cousin of Aaron Hernandez, said Bristol Police Lt. Kevin Morrell.
Alcorn was also the man nicknamed "Chicago" in a Massachusetts state police report that was listed as the possible source of a .38-caliber gun seized from a car after a June 21 accident in Springfield, Mass., according to Morrell.
Hernandez, a Bristol native, has pleaded not guilty and is being held without bail on a first-degree murder charge in the death of Odin Lloyd, an acquaintance and semipro football player who police said was shot five times in an industrial park near Hernandez's North Attleborough home in June.
Hernandez's lawyers have called the case circumstantial and said their client looks forward to clearing his name.
Hernandez also has been linked to the investigation of a 2012 case in which two men were shot near a Boston nightclub. While probing the Lloyd shooting, police found an SUV, sought in the double homicide, at the home where Tanya Singleton lived with her uncle in Bristol. The vehicle had been rented in Hernandez's name.
Massachusetts authorities have not commented on the nature of the grand jury. A grand jury in another Massachusetts county has already returned indictments related to Lloyd's death.
"I can say my client has no connection to any weapons," Dyer told WFXT-TV after leaving the courthouse Thursday. He would not say whether Alcorn testified before the grand jury, but said he was cooperating with investigators.
"He's cooperating in the spirit of the law, everything he needs to do he's doing, so I can't tell you anymore about what he's doing or what's he's seeing, what he's done, or what he's going to do but we're cooperating."
On Tuesday, a Superior Court judge in Connecticut ordered Alcorn to appear before the grand jury. Judge Joan Alexander also issued a warrant allowing police to arrest a second man, Alexander Bradley of East Hartford, and compel him to appear before the same grand jury. Bradley did not appear at the Tuesday hearing to show why he should not be required to testify.
Thaddeus Singleton III was killed in June when the car he was driving slammed into a country club building in Farmington, Conn. Police have ruled the death an accident.