Generally speaking "hometown" tends to refer to the place you were born and raised in rather than where you currently live; however that may depend on where you are geographically at the time you say it!
- If you were at university in London and you said "my hometown is Liverpool", it would be understood that you normally live in Liverpool but you are temporarily residing in a different place for your education.
- If you were permanently living in London and said "my hometown is Liverpool" it would be understood that you were born and raised in Liverpool but now live in London.
- If you were visiting London and said "my hometown is Liverpool" it would be understood that you normally live in Liverpool, not necessarily that you were born there.
To clarify what I mean by "born and raised" - it is entirely possible for someone to be born in one place but mainly raised in another - for example, if your parents lived in Liverpool at the time of your birth but your mother suddenly went into early labour whilst visiting London, you might end up being born in a London hospital with 'London' as the place of birth marked on your birth certificate (in the UK at least), yet you may never spend any of your childhood there. In those or similar circumstances, your "hometown" is where you were raised, and your place of birth is largely irrelevant to this.