If you're suspicious, or uncertain whether you should believe something (or someone), you're distrustful. If your dog is distrustful of clowns, she may growl every time she sees anyone wearing a big, red, rubber nose.
Whenever you experience a lack of trust, you're distrustful. The word adds the prefix dis-, "not," to trustful, or "full of trust." If your cousin frequently tells tale tales, you will probably be distrustful when he claims that he recently met a famous movie star. And if that old wooden roller coaster at the amusement park looks rickety, you might be distrustful of its safety go ride the merry-go-round instead.