public Guid TaskItemGuid {get;}

// find the first project task item which is open
var taskItem = Project.Current.GetItems<TaskProjectItem>().FirstOrDefault(t => t.IsOpen == true);
// if there isn't a project task item, return
if (taskItem == null)
  return;

// close it
// NOTE : The task item will also be removed from the project
TaskAssistantModule.CloseTaskAsync(taskItem.TaskItemGuid);