“I’m not prepared today to say what we’re going to do,” he said.

Mr. Garabedian wrote in a court filing that the accuser’s mother, Heather Unruh, delivered the smartphone to the police in December 2017, toward the beginning of the investigation. The police said that the phone had been returned to the young man’s father, Mr. Garabedian wrote, but the father did not remember receiving it.

The family had searched “all the places where such a phone may have been stored,” Mr. Garabedian wrote, but they were not successful. At Monday’s hearing, Mr. Garabedian said they had recovered a backup of the accuser’s phone on his laptop that covered the time of his encounter with Mr. Spacey. It was not immediately clear if the backup preserved any of the potentially missing messages.

After being given the opportunity to follow her son’s lead and plead the Fifth, Ms. Unruh, a former television news anchor in Boston, waived that privilege and took the stand.

“I have nothing but the truth to tell,” Ms. Unruh told the judge, her voice cracking.

Ms. Unruh testified that she had looked at her son’s phone before she gave it to the police and deleted some content that “concerned” her as a mother. The state trooper who received the phone from Ms. Unruh testified that Ms. Unruh had told him that she had deleted some content regarding “frat boy activities” that she did not want investigators to see.

She said that she had never instructed her son to delete any messages, and never deleted any messages herself from the conversations that Mr. Spacey’s lawyer was concerned about.

“I didn’t touch anything that was relevant to the case,” Ms. Unruh said.

The accuser’s father also took the stand, testifying that he did not remember ever getting the phone back from police. (The New York Times is not identifying the father, who has the same surname as his son, to avoid naming an accuser in a sexual assault case.)