If the statement wasn't intended as question but the intonation was similar to one, that's uptalk, which is a feature used by some speakers of some dialects (or idiolects). According to Wikipedia:
The high rising terminal (HRT), also known as upspeak, uptalk, or high rising intonation (HRI), is a feature of some variants of English where declarative sentences can end with a rising pitch similar to that typically found in yes-or-no questions. HRT has been claimed to be especially common among younger speakers and women, though its exact sociolinguistic implications are an ongoing subject of research.
If it was intended to be a question, that's just a feature of English. I'm not sure that there's a single name for non-inverted questions (actually, "non-inverted questions" is a pretty good name), but some of them are echo questions:
We use echo questions to repeat part of what we have just heard when we don’t fully understand or when we want to confirm what we have heard. We use rising or fall-rising intonation:
Did you hear Pete’s giving up his job.
Pete’s giving up his job?