Last week, that employee, Dorothy Smith, a credentialing specialist at the center in Mandeville, La., and 30 other people were indicted in the scheme, prosecutors said on Monday.

According to the U.S. Attorney’s Office for the Eastern District of Louisiana, Ms. Smith worked with intermediaries to secure bribes. Two former Coast Guard employees are among the six intermediaries whom prosecutors said Ms. Smith used as part of the operation. The other four, who were workers in the maritime industry, had their scores fixed by Ms. Smith in addition to recruiting others.

In exchange for the bribes, Ms. Smith falsely reported that the applicants had earned passing scores on exams or learning modules, prosecutors said, and in some cases reported that the applicants had appeared for the tests when they had not.

The exams test “mariners’ knowledge and training to safely operate under the authority of licenses,” according to a statement from the U.S. Attorney’s Office.

Ms. Smith and the six intermediaries were each charged with conspiracy to defraud the United States. A lawyer representing Ms. Smith in the case declined to comment.

The scheme “resulted in the applicants illegally obtaining a range of licenses for officer-level positions, including the most important positions on vessels, such as master, chief mate, and chief engineer,” the statement said.

The Coast Guard did not immediately respond on Tuesday night to a request for comment.

Twenty-four other people face charges in the case. They were charged with receiving, possessing and intending to unlawfully use mariner licenses by way of the false scores. Some applicants had their scores fixed on multiple occasions, prosecutors said.

One applicant paid an intermediary $3,500 for fake scores, according to the indictment. Another paid Ms. Smith $1,000 directly, prosecutors said. They did not say how much Ms. Smith and her associates made in the scheme.

If convicted, each of the 31 defendants could face up to five years in prison and a $250,000 fine, prosecutors said.

The case is being investigated by the Coast Guard Investigative Service. It was unclear how investigators became aware of the operation.

The indictment came more than a year after dozens of people were charged in an unrelated widespread college admissions cheating scandal. Those charges resulted from the Justice Department’s “Varsity Blues” investigation and involved celebrities including the actresses Felicity Huffman and Lori Loughlin.

The investigation revealed that wealthy parents had paid to have their children’s admissions scores fixed, sometimes in conjunction with falsified résumés and bribes to coaches to admit students as competitive athletes.

Last week, a former fencing coach at Harvard was accused of taking $1.5 million in bribes to assist a wealthy Maryland businessman’s sons in being admitted to the school.