Checklists - dillenmeister/Trello.NET GitHub Wiki
Example on how to check all unchecked check items on a card's first checklist.
var card = trello.Cards.WithId("x");
var checklist = card.Checklists.First();
foreach (var checkItem in checklist.CheckItems.Where(ci => !ci.Checked))
trello.Cards.ChangeCheckItemState(card, checklist, checkItem, true);