Is it appropriate to use "Hey yourself"?

Some people consider hey to be an inappropriate greeting ("Hay is for horses"), but among those who do not, I wouldn't say that hey yourself has any inherently negative connotation. Its meaning is literal: hey to you as well

I could say it dismissively or menacingly, but also flirtatiously or cordially. In such casual exchanges, the tone, tempo, body language, and other cues will impart far more meaning.

Of course it would depend on the speaker (tone and attitude) and some special situation you might have. If you want it to become a cold greeting, that's up to you as well.

But the expression "Hey yourself" per se just means "Hello to you too."

It's a casual expression so you can take that into account. It's the same as "Hello/ Hi back," which is another innocent greeting.

I've only heard this phrase used a few times, and it was always used negatively. Some people consider "hey" a rude greeting, so if someone says it to them, some reply "hey yourself". It would be similar to someone yelling, "You're stupid, Bob", and Bob replying, "No, you're the one who's stupid".

That said, if someone said "hey yourself" to me in a cheerful tone of voice, etc, no indication that they were insulted or attempting to be insulting, then I would take it as equivalent to "hello to you too".

(As to why some people object to the greeting "hey" ... Like many words, what is polite and what is offensive is a matter of social convention, not any rigorous rules of logic.)