It is unclear whether any conclusion will be reached before the presidential election on November 4.
Palin's leadership was questioned earlier this month in a legislative report that found she violated state ethics laws by letting a family dispute influence her decision-making.
"I make no apologies for wanting to protect my family and wanting to publicise the injustice of a violent trooper keeping his badge"
Todd Palin, husband of Sarah
The report found that Monegan's firing was proper but that the pressure she applied to fire Mike Wooten, the policeman, was not.
Although the report issued a stinging rebuke of Palin's conduct, it carried no penalty.
It is up to the Alaska personnel board to decide whether Palin violated the law.
Unlike the legislature, the personnel board is run by officials that Palin can fire but only for cause.
"I am so pleased to finally have gotten the chance to tell what really happened and get the truth out," Palin said in a statement released by her attorney.
"It was the right thing to do to bring this before the personnel board and have a true arms-length unbiased and apolitical investigator look into this."
The Monegan controversy, known as "Troopergate", took on national significance after John McCain, the Republican presidential candidate, selected Palin as his running mate.
Griffin Taylor, a McCain campaign spokesman, says Palin stands by her decision to fire Monegan and her concerns about Wooten.
Palin and her husband, Todd, say Wooten had made threats against their family. Wooten had also used an electric stun gun on his stepson.
"I make no apologies for wanting to protect my family and wanting to publicise the injustice of a violent trooper keeping his badge," Todd Palin said in an affidavit submitted to legislative investigators.
Thomas Van Flein, Sarah Palin's attorney, characterised the Alaskan governor's testimony to the independent investigator as "thorough, candid and detailed".
Van Flein said Petumenos assured him he was working quickly but made no promise the case would be closed before election day.
"I just hope the truth comes out," Van Flein said. "If it's after the election, it's after the election."
Whether Palin's testimony will become public remains uncertain.
Personnel investigations are normally secret and, though Palin has waived her privacy rights, others in her administration have not and Petumenos has sought to keep the matter from playing out in the media.
Van Flein said Palin would like to release a transcript of her deposition, but producing one typically takes days and it is unknown whether Petumenos will allow it.