This actually applies to all i-adjectives, not just たい forms:
Positive: 青いです
Negative: 青くありません、青くないです
(It doesn't apply to -ます verbs, though: 食べません, not 食べないです... though I think the latter does occur in some dialects and maybe really colloquial speech, just not Standard Japanese)
I
think -- I'm ridiculously far from an expert, here -- that the difference between the ないです and ありません forms is more a matter of formality than politeness, which is slightly different (though obviously the two overlap heavily). For instance, the way you talk to a stranger in the street, though it may be very polite, tends to be less formal than the way you'd talk to somebody in writing, or in a formal ceremony. For instance, using contractions in English ("it's", "I'm", etc., etc.) is informal, but not impolite.
I've had people correcting my Japanese writing on the web change 青くないです to 青くありません and I've had others do it the other way around. Sometimes you can't win, really.
