The trick with subjective adjectives like ほしい is that when you want to use them for someone else, you need to use the auxiliary verb ～がる = shows signs of ~. The reason for this is that you are not them, so you don’t know for sure that that’s what they’re thinking. A fair percentage of Japanese grammar involves taking the appropriate perspective on a situation.

The formation is Adjective-stem+がる
For example:
ほしい -> ほしがる
食べたい -> 食べたがる
めんどう（な） -> めんどうがる

It conjugates as an う-verb (i.e. がる -> がった -> がらない -> がらなかった)

So, getting to the sentence at hand:
ひとみさん　は　くるま　を　ほしがらない = Hitomi-san shows signs of not wanting a car = Hitomi-san doesn’t want a car (The particle is を because it’s a verb now)

You can use ほしい as-is when asking someone else what they want:
ひとみさん　は　くるま　が　ほしい　ですか？

You can also say:
ほしい　と　思う = I think she wants
ほしい　と　言った = She said she wants
ほしいそう = I heard she wants
ほしい　かもしれない = She probably wants

Et cetera.

In-depth enough for ya? =P

Brook wrote:

Use with ほしい, use with a verb + たい, use with a -な adjective…

Not exactly. It’s used with a fairly specific group of adjectives, which the grammar dictionary describes as “psychological / physiological”. It goes on to give a list of adjectives for which it’s frequently used, including うれしい, こわい, おもしろい, いたい, さむい, くるしい, めいわく and いや, among others. Most of them are い-adjectives, simply because most emotive adjectives in general are い-adjectives.

The end result of a Verb+たい construct, incidentally, is an い-adjective, which makes for a real weird back-and-forth in parts of speech:
食べる = verb
食べたい = adjective
食べたがる = verb again

Just to be 100% sure, though… You’d still use がる if you were to ask someone what someone else wants, right?

Interesting question. I have to admit, I’m not entirely sure either, but I’d be willing to hazard “yes”.