The D.C. Council will ask a city judge to order three key figures to cooperate with its investigation of Mayor Vincent C. Gray’s hiring practices, after a unanimous vote Tuesday authorizing court action.

Sulaimon Brown, the central figure in allegations of payoffs and job deals extended by members of Gray’s campaign, has refused to testify. He has questioned the motivations of the council’s probe, led by member Mary M. Cheh (D-Ward 3).

Cheh’s government operations committee hired process servers, at a cost of $2,000, to summon Brown and Cherita Whiting, a Gray supporter who was given a mid-level job with the city parks department, to appear at a May 13 hearing, but neither was successfully served in person. Cheh then sent the subpoenas by certified mail, as is permitted under council rules. But neither witness showed up at Friday’s hearing, where Cheh said they “appear to have been evading service.”

Both Brown and Whiting have acknowledged in interviews that they are not voluntarily cooperating with the investigation, which has been widely publicized. Both also say that they did not receive a summons.

“If she can lie about something as simple as issuing me a subpoena, it’s obvious she can’t be trusted,” Brown said. “I believe she’s trying to help Vincent Gray cover it up.”

Brown declined to say whether he would obey a court order, but Whiting said that if a judge orders her to testify, she will. “I still don’t have any answers for them,” she said. “I didn’t work in HR. I got my job the right way: I filled out an application, I had an interview and I got hired.”

The council also voted to force the testimony of Peyton M. Brooks, son of Howard L. Brooks. Howard Brooks is alleged to have delivered cash payments to Brown. (The Washington Post has been unable to independently verify those payments.)

Cheh asked both father and son to testify, but both declined, citing their constitutional right against self-incrimination. Cheh excused the senior Brooks, but she is questioning whether the son is entitled to broadly cite Fifth Amendment protections.

Brooks’s attorney, Troy W. Poole, declined to comment.

In coming days, council attorneys will ask a D.C. Superior Court judge to order the three to appear before the council. If orders are granted, and if the witnesses flout them, they could face fines or be found in contempt of court and face criminal sanctions.

While the subpoena wrangling represents an obstacle to the council’s investigation, there are new signs that federal authorities have accelerated their criminal probe. Previously, the U.S. attorney’s office said that it was “assessing” the matter.

On WTOP radio Tuesday, Gray said that he has voluntarily turned over e-mails and phone records to federal authorities but that he had not been interviewed.

Kenneth V. Cummins, a private investigator who did vetting work for the Gray transition, said that his firm, Capitol Inquiry, turned over e-mails and 41 completed background checks pursuant to a federal subpoena issued last month.

“Quite frankly, I don’t think there’s anything in what we provided that warrants any kind of criminal investigation,” said Cummins, who said he had been in touch with federal investigators as recently as last week.

Friday’s council hearing came to an abrupt aide after Lorraine A. Green, the head of Gray’s campaign and transition, declined to answer questions about the elder Brooks, citing the active federal probe. Thomas C. Green, her attorney and no relation, told council members that the U.S. attorney’s office “will more likely than not want to talk to her” again.

The House Oversight and Government Reform Committee is also looking into Brown’s allegations. Gray, Green and Brooks have denied Brown’s claims.

Gray said in his radio interview that he has “urged everybody to participate and cooperate with the investigations.”

Staff writer Nikita Stewart contributed to this report.