A race in my WIP has a humanoid torso and a quadrupedal lower body. I like the look of the Japaneses Bow and I was thinking of having it be developed by the centaur-like race. It is theories that the shape of Yumi is in part do it meant to be wield from horse back. Since a centaur-like race is naturally in the "mounted" position. It made sense to me that if the theory about the Yumi's design were true, then a centaur-like race would hit upon that design.
A humanoid mounted on a quadruped has to deal with the front half of said mount's body, plus said mount's head, being in front of him. This is an obstruction that a centaur-like race simply does not have to deal with; in fact, as far as what's in front of the humanoid torso of a centaur, there's really very little that's any different from a regular humanoid.
The long and the short being that a centaur would in all likelihood use a bow similar to that used by a non-mounted humanoid, as they do not have the same obstructions to deal with as a mounted humanoid.
That said, a yumi-style bow has advantages apart from maneuverability on horseback. Larger bows are (in general) more powerful. But if you get too large, you have the lower tip hitting the ground or tripping you up as you try and move through anything other than the flattest of plains -- especially if you're shooting while on the move. So a yumi-style bow gets you the power of a large bow without tripping you as you run across the battlefield.
The takeaway is that if you want your centaurs to use yumis, have them use yumis. It's got advantages even if the considerations of a mounted human don't apply to centaurs.
I have thought about this before. As I understand it, the yumi-type bow is wielded "long side up" so you can get maximum power without, as mentioned, the bottom of the bow hitting the ground (and y'know, Japanese people aren't super tall). A centaur would have the opposite deal, he's so tall (try drawing one where he's the same height that an equivalent human would be, you'll see it looks lousy, the human part looks oversized) that he could flip the yumi-type bow "long side down" and get maximum power without.. y'know, hitting power lines. Or just so his bow isn't stupidly long and he has nowhere to put it. But without knowing the actual physics, I couldn't tell you whether, say, a 4-foot symmetrical bow and a 4-foot asymmetrical bow have the same power or which one is stronger. The point of the asymmetrical one is "if you tried using one this long from the middle, you'd hit the ground"
.. now the real question is whether a multi-armed guy could use two bows at once