Or does it have to be through the legislature or state conventions
Not directly through a ballot measure, but I remember looking at Minnesota (I think it was) election law way back and seeing something that seemed to suggest there would be an effective ballot vote when Congress went the state convention route (slates of state convention candidates, I think elected statewide (so no "electoral college", or rather an electoral college of people pledged to vote the same way as the statewide vote)).
But I remember reading that in some states it's been decided somehow that the Legislature would
be the convention for ratifying a U.S. constitutional amendment if Congress chose the convention route. I'm not sure if that would be all Legislators voting in one body in convention or if it would be the traditional bicameral Legislature. Heck, I'm not 100% sure how that works when the Legislative ratification route is used, although I think separate favorable votes in each chamber are required (apart from Nebraska's unicameral Legislature).
So in short, in some states effectively yes (I think), in others no. But strictly speaking, no everywhere.
