In the ongoing legal dispute over control of the historic Mukai house and garden, the nonprofit group Friends of Mukai will go to court again next week.

The Court of Appeals will hear oral arguments about the case on Tuesday, and islanders are asked to attend the proceedings.

“We want the court to understand it means a lot to Vashonites,” said Lynn Greiner, an attorney with the friends group.

Tuesday’s hearing is expected to be brief, Greiner said, as each side is given just 10 minutes to present its case.

The hearing could bring an end to the long-standing legal dispute that began in 2012, when the friends group formed and asserted its control of Island Landmarks, the entity that owns the historic Mukai house and garden. The group contended then — and continues to contend — that  Mary Matthews, who established Island Landmarks in 2000, has not fulfilled her obligations by not opening the home and garden to the public and allowing the property to fall into disrepair. Matthews also owes $17,000 in back taxes, Greiner said.

Matthews has frequently denied allegations of wrongdoing and has fought to maintain ownership of the property.

Last April, in trial court, judge Monica Benton ruled that the community members of the friends group are the “lawful governing board” of Island Landmarks, but Matthews appealed.

Now heading to court on that appeal, Greiner said the friends group is in a good position,  and members believe they have a strong case in part because Benton made her decision based on considerable evidence, and there is a legal presumption that the trial court made the right decision. Greiner also noted that Matthews’ attorneys recently withdrew from the case after representing her for more than a year.

A three-judge panel will decide the matter, though a decision might not come until summer.

The court is located at 600 University Street in Seattle; the courtroom is on the main floor. The hearing is scheduled for 9:30 a.m.