This seems like a straightforward question, but it doesn't have a straightforward answer.
I'm going to assume we're talking about a backhandspring on floor, and that your goal is to do it in connection, not in isolation. And I think backhandsprings make the most sense when you think of them first in terms of the mechanical goal of the skill, which is to accelerate backwards as much as possible.
In order to accelerate backwards, you want to exert as much force on takeoff as possible. For that, you want your entire body to be contributing everything it can, including lower body, midsection, and upper body and arms. In order to do that, your legs should bend, your midsection should sit way back behind your feet (you feel like you're about to fall on your butt just before you take off), and your arms should be in front of you and perhaps angled slightly downward; from there, everything extends at once to generate the acceleration and rotation for the backhandspring. All of this is true whether you're doing to backhandspring in isolation or in a connection. (Somewhat different on beam, but I assume we're focusing on floor here).
So to answer your question about the arms, they should be extended in front of you (horizontal or a little bit below) and then they should swing upwards towards the ears as you take off.
Having said that -- there's room for debate over whether you should start with the arms held in that position, or swing them through that position. I generally teach the former just to keep things as simple and minimal as possible, but I don't hate the latter.
There is some nuance I'm glossing over here. I like arms starting in front specifically because I assume the goal is to do it from a roundoff -- if you're only looking to do it from a stand, an arm swing will probably get you there faster. And if you're doing it to a stepout, or if you're doing it on beam, or if you are for whatever niche reason trying to make your backhandspring very short, the ideal technique changes.