So, what was it?
Kate guessed that it's a weaving tool. This is a really good guess. And for all I know, it might be. It certainly bears some resemblance to descriptions of weaver's combs I've found online (the one linked to does not resemble this object, but it's a starting point, if you're interested). But I can't know if Kate is right.
The museum's records tell me only that this is "Northwest Indian bone comb or fork." These records are incomplete; the donation was purchased decades ago by the museum, after the collector has passed away so the information is incomplete at best. In fact, it's the same collection as the awl from two weeks ago, and it has the same problem.
Personally, I really like this object. And I really wish I knew more about it. Until the time that this collection is researched by experts, we probably won't be able to identify its original purpose.