"Your hair needs cut" is a more informal way of saying "your hair needs to be cut", although many UK native English speakers would say "your hair needs cutting".
More informal ways of saying the same thing are "you could be doing with a haircut/you need a haircut".
In fact, "your hair needs to be cut" is too wordy and formal, and comes across as awkward. Although grammatically correct, I can't imagine a native speaker ever saying it spontaneously.
As the Eagle Flies - Page 331 - Google Books Result
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J. D. Oliver - 2012 - Fiction
Faith tossed me a bar of soap, “Wash your beard, you had food in it. Your hair needs cut, probably in the morning I'll cut it, when I trim your beard.”