I main both of them so I'll give out some insight on the MU.
First, let's start with the man in green.
: Luigi can ko better, combo the h*** out of her, has better grab game, and throws. Luigi's fireballs are vertical so if you miss the fireball with Luma's jab, then Rosalina may get hit. Even if you shield the tornado, Luma will still get hit. Forward smash and Neutral attack Luma off the stage to focus on Rosalina. Also, damage output surpasses Rosalina's and can put on hurt Luma .Once you get grabbed, you're combo meat because of her big and tall hurtbox. The tornado set-up is helpful too because she's floaty and have a large hurtbox so you'll have a hard time di-ing out of it. Up-b can kill Rosalina at 64% or higher if you get read, or when he finds a hard punish. Rosalina is floaty and her landing options aren't safe so don't land on Luigi unless you want more damage from him. His ko moves are better than your along with rage because she's light and floaty. Off-stage, down-air for spiking, back-air for stage spike, f-airs, and the tornado(without jump for button mash) are something to watch out for since she doesn't have a hitbox on her recovery. Also, ledge punishes from his down-smash(which can spike her down), and down-tile are something to look out for while recovering. Pivot grab, pivot fireballs, pivot up smash and forward smash are something to look out for since he can slide alittle more with bad traction. Best not to use GP against fireballs because of her end lag and short range of the fireball. Watch out for his grab because he'll go for a back throw to split R&L to get rid of Luma since the star can't stop the grab and won't go for pummels or his down-throw with Luma around.
: Her range, dangerous edgeguarding, and jiggling game can be a huge threat, here. Luma's jabs can snipe out approaches because they're bad. Forward tile and down tile to out-space and shut down his approaches with her range. SH n-air, Neutral b, and SH b-air for zoning and out-spacing him. With Lunar landings, you can bait, out-space, mindgame, and even get a small combo as well. Up-tile and up-smash serves as anti-air moves against Luigi's low range aerials and tornado. Since Luigi is floaty and has poor air speed, she can jiggle him hard with up-airs and give him trouble, landing. Use her dangerous up-airs to get combos, harass him above you, frame trap him, and even get early kills with Luma(rage to add). Use Luigi's bad traction to your advantage because if he raw shield, then he'll get push back and slide farther to actually punish. Star bits help for spacing along with Lunar landing. Rosalina's edgegurading hurts Luigi more than Mario because of his jump punch less jump height, and linear recovery. Green missile to easily get spiked down by down-air on Rosalina's hitbox. Even to get a early kill or gimp with down-air on Luma's hitbox. B-air to punish the end lag on the tornado if you get a read. Her ground speed is better than Luigi along with air speed, but not greater though. Down smash for killing by its back hit, spacing, and ledge punishing along with down tile, and angled forward smash. Mix up approaches, make it hard for Luigi to approach you since he's bad at it, zone and space him out pivot forward tile, pivot forward smash and pivot up smash, and use her range to your advantage along with Luma.
Stages: Battlefield is a must because Rosalina can harass Luigi even more with platforms by jiggling him with up-airs, SH aerials, star-bits, up-tiles, up-smashes, and give him trouble landing from platforms to the ground. So thank her tall height and range. As for Luigi, blastzones help him live longer and even get more combos from platforms. Delfino Plaza and Helberb are worst for Luigi because even though Luigi's vertical ko can kill earlier, Rosalina can also kill early with vertical kills as well with using platforms to her advantage. Duck hunt is ok for both because of bigger blastzones and no stage spike kills. However, since there's room to run around, she can run away, camp, and also use the tree under for up-airs against Luigi. Lylat criuse must be ban because the stage moves and can mess up Rosalina's recovery for her to snap the ledges.
Customs: Shooting star bit because you use as a projectile for damage, camp, pivot, and force approaches. Crouch is not low enough to duck under shooting stars. Guardian Luma for Luigi's incoming attacks, mindgame, and spacing. Teleport Luma for more options to gimp, set ups, and mindgames.
Results: +2 in Rosalina's favor because
may have better damage output, combos, air game, and koing, but Rosalina's disjoint range, zoning, jiggling game, and edgeguarding game are dangerous against Luigi and she's a threat to him. She may be one of his hard MUs because of her threating tools so its hard for him to get grabs on you.
As for customs, I'm going to say its +2.5. With shooting star bit, its better than Luigi's fireballs, she can use them to camp, stop approaches and force Luigi to approach you even if he power shields them. Teleport Luma to gimp for early kills if possible and mindgame. And Guardian Luma is better than default since it give Luigi more trouble approaching with baits, mindgames, and spacing.
Sorry, Luigi players, but as both a Luigi and Rosalina main, I have to argee this MU favors Rosalina and she can give Luigi h***(but less than Sheik though) if you face really good Rosalina player and they know what they doing. Please prove me wrong if any of you Luigis out there have good information on the MU and I'm missing something.
As for Rosalina players, have fun with the MU and do your best, giving the man in green a rough time on the battlefield.
Edit: @
Mario & Sonic Guy
I change my score for the customs to +2.5 instead of +3. Default score is still the same. Yeah, I think +3 was too much so I went to +2.5 in Rosalina's favor for Customs because I think its that score at best. Sorry for the confusing and I could ask if you can change my score for Customs on the spoiler list.