It's not possible to assign tasks to other users in RTM, but you can share or send them. You can then use the advanced search operators to search for tasks that have been sent to or shared with a particular contact. Hope this helps!

Emily, this brings up a point that I forgot about. I haven't used share and send much, but tried it out recently. I first shared a task with my wife, then I sent the task to her. I'm assuming that normally send removes it from your lists, whereas share keeps it and just makes a copy of it in another user's list. But when I did the share and then send, it wouldn't go away from my list, presumably because I already shared it. So my take on this is that share and send should be mutually exclusive, right? You either share a given task with someone or you send it to them? If so, there might be a bug here in that it's letting you do both.