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The two rarely interact in canon.
In Chapter 1, before the murder happened, Kirumi and Tsumugi were together in the dining hall, along with Korekiyo Shinguji and Miu Iruma.
In Chapter 2, Kirumi told Tsumugi to wait with discussing the Motive Video until everyone gathers in the dining hall. When everyone was using Kirumi to do their chores, Tsumugi was the first one who noticed so and called them out on it. Excluding Tenko Chabashira, who only didn't want Kirumi to spoil the boys, she was the only one to react to it. However, Kirumi assured that she loves serving people. After Ryoma had been eaten by piranha's, a distraught Tsumugi is shown being comforted by Kirumi during the closing argument of second-class trial.
During Chapter 3, Tsumugi at some point stay's she's glad that she was just an average citizen and that if she ever had a will to live as strong as Kirumi's that she would just cower in a corner somewhere, unable to bear the responsibility.
In Danganronpa V3: Killing Harmony (Demo Version), Tsumugi thinks that Kirumi's work as a maid is super cute.
In one of the optional dialogues in her Love Across the Universe events with Shuichi Saihara, if Shuichi suggests baking together, Tsumugi tells him to ask Kirumi to do that instead as her own baking would just be boring.
In one of manga adaptations, Tsumugi made Kirumi and Maki cosplay together.
The ship sailed as a result of Tsumugi standing up for Kirumi when everyone kept using the latter to do their chores.
Being a ship that resulted from minor interactions, it's not that popular and only a small part of the fandom is even aware of it. Nonetheless, it is still quite popular for a minor ship. However, with the reveal that Tsumugi was the mastermind and didn't really care for anyone, many of its shippers abandoned the ship.
- Tsumugi – “When I woke up, there was a Kubs Pad in my room, but the video on it wasn't even mine-”
- Kirumi – “Tsumugi, we should discuss this once everyone is here.”
- Tsumugi – “Oh, sorry... You're right.”
- — Kirumi tells Tsumugi to wait with discussing the second motive.
- Tsumugi – “You guys are relying on Kirumi too much.”
- Kirumi – “I do not mind... Serving others is the true desire of any maid.”
- — Tsumugi standing up for Kirumi when everyone uses her for doing their chores.
- “If you want to do things like that, you should ask Kirumi. Even if I made it, it'd just be boring.”
- — Tsumugi suggests Shuichi to ask Kirumi to bake together instead, knowing that her baking isn't "boring," in an optional dialogue in Love Across the Universe.
- With the reveal that Tsumugi was actually the one who killed Rantaro instead of Kaede, both were the culprits of back-to-back chapters.