To be evasive is to avoid something, whether it's a touchy subject or the person who's "it" in a game of tag.
If you're dodging the truth and not giving straight answers, then you're being evasive. Which is probably not the best strategy when the police are asking the questions. From the French évasif, it’s an adjective that describes someone who's being intentionally shifty or vague. But a concept that’s hard to pin down or comprehend can also be considered evasive.
