Answer:
When you think of a word and its connotation (if any exists), use it out loud. You'll have to add things to make a sentence, but ignore the parts you add; instead, focus only on the word.
So, you've asked if "happen" has a positive, negative, or neutral connotation. Try these sentences, ignoring the part that is in parentheses.
(I) happen (to know them).
(She asked what would) happen.
(The boys asked, "When did it) happen?"
(The trial will) happen (soon).
Review those sentences, focusing only on the word, "happen". What emotions do you have when you hear only the word "happen" (just "happen", don't add to the word).
If you said, "Nothing," or "It means nothing to me", that's fine. Your reaction helps tell you that the word "happen" has an absolutely neutral connotation.