MADISON, Wis. — The grandfather of a northwestern Wisconsin girl who authorities say was abducted during a home invasion that left her parents dead said Saturday that the family has no connection to the suspect and doesn’t understand why he targeted her, deepening a mystery that has captivated the state for months.

Someone blasted open the door of James and Denise Closs’s home near Barron with a shotgun in October, gunned the couple down, and made off with their 13-year-old daughter, Jayme Closs.

Jayme had been missing for nearly three months Thursday when she approached a stranger near the small, isolated north woods town of Gordon and pleaded for help. Officers arrested 21-year-old Jake Thomas Patterson minutes later based on Jayme’s description of his vehicle. He was jailed on suspicion of kidnapping and homicide.

Investigators have said Patterson’s goal was to kidnap Jayme, but he appears to have no connection to the family. Jayme’s grandfather Robert Naiberg said in a telephone interview Saturday that the only thing the family knows for sure is that no one knew Patterson. He said Jayme told FBI agents she didn’t know him at all.

‘‘He didn’t know Jayme, he didn’t know Denise or Jim,’’ Naiberg said. ‘‘[Jayme] don’t know him from Adam. [But] he knew what he was doing. We don’t know if he was stalking her or what. Did he see her somewhere?’’

Attorneys for Patterson called the affair ‘‘a very tragic situation’’ and said they were relying on the court system to treat him fairly. Charles Glynn and Richard Jones said in a statement that they await Patterson’s initial court appearance and the filing of charges against him on Monday.

The news that Jayme was safe set off joy and relief in her hometown of Barron, population 3,300 and about 60 miles from where she was found. The discovery ended an all-out search that gripped the state, with many people fearing the worst the longer she was missing.

Jayme’s aunt Jennifer Smith posted on Facebook Saturday that Jayme was doing well.

‘‘Jayme had a pretty good night sleep it was great to know she was next to me all night what a great feeling to have her home. As a family we will get through all of the healing process Jayme has. It will be a long road but we are family strong and we love this little girl so much!!’’

Another aunt, Sue Naiberg Allard, posted that Jayme got ‘‘the most awaited hug ever’’ when she returned home.