Only if you put the subject היא in front. Third person past tense verbs require an explicit subject. Without that subject, we're talking about the noun החליטה, meaning "decision", and not about a conjugated verb.
Not quite. החליטה is indeed the past tense form, as DL-Trolls suggested. The noun "decision" is החלטה - there is no yud, nor is there need for it, since the word has only "a" vowels - hachlata. It's a mistake.