WASHINGTON — The State Department said Tuesday it had no record showing that Hillary Rodham Clinton signed any official statement attesting that she had turned over all unclassified documents related to official business when she left her post as secretary of state in 2013.

Department spokeswoman Jen Psaki said that Clinton’s two immediate predecessors, Colin Powell and Condoleezza Rice, had not signed such a statement either.

Psaki said there was no sign of such a statement in department files.

“We’re fairly certain she didn’t sign one,” Psaki told reporters. Psaki said that even though it was “not clear” that such statements were used throughout the federal government or even inside the State Department, she said that department officials were still trying to assess whether Clinton and former secretaries of State should have signed the documents.

The State Department requires employees leaving the diplomatic service to fill out an official statement — known as form OF-109 — acknowledging that they have turned over all classified and unclassified records of government business to “responsible officials.” But Psaki said that different bureaus within the department had varying rules relating to such statements, effectively making it optional for some employees to fill them out and turn them in. She could not identify the bureaus in which employees had such a choice.

Questions about whether Clinton signed such a document have swirled since the revelation of her use of a personal email account for government-related work. Republicans and other critics have said that the State Department, along with other federal agencies, generally requires outgoing employees to turn over job-related materials before leaving — and that Clinton also should have met that standard. Federal policy generally requires employees to sign such separation statements declaring they have turned over all documents relating to official business during their employment. Providing incorrect information on the form can be grounds for prosecution.

The office of House Speaker John Boehner, R-Ohio, said in a statement on Tuesday that it would be “a big problem if she signed that form like she was supposed to.” Others have said it would be equally troubling if Clinton did not sign the form because that would have meant she would was holding herself to a different standard than other employees.

Psaki said that Clinton’s failure to sign such a statement was “not a violation of any rule” and did not risk any department punishments. She noted that “there are differences between regulations and recommendations,” and added that “we’re not aware of any penalty for not signing it.”

The OF-109 form lists several U.S. Criminal Code violations involving classified materials and government records but does not cite a warning for failing to sign the statement.

Guidance from the National Archives and Records Administration says that personal files may be removed by departing federal officials but that “if you are unsure whether materials are personal or federal records, consult with the agency records officer.” NARA also says that “when determining whether to permit departing officials to remove documentary materials, the agency should also consider the extent to which such removal could affect the agency’s ability to invoke various legal privileges.”

Other agencies have specific rules governing the removal of government files. The Department of Homeland Security, for example, advises that agency records officials will obtain “signed removal forms” from all presidential appointees and that “records will not be disposed of while they are the subject of a pending request, appeal, subpoena or lawsuit under the Freedom of Information Act or the Privacy Act.”

The Republican National Committee earlier Tuesday submitted two Freedom of Information requests to the State Department seeking copies of the “separation statements” signed by Clinton and her top aides and related records.