Origami one-sidedly proclaims herself as Shido’s girlfriend or lover unbeknownst to Shido himself. Origami uses any chance she gets to make her relationship with Shido more intimate. Her love for him is quite unhealthy as she often disregards most of Shido's feelings or opinions and can come off as self-centered.
In reality, Origami is a stalker with Shido being the focus of her desires. She has secretly been following Shido around in his everyday life since before the start of the series and has on many occasions tried seducing him with her actions, such as buying a new bed, making herself deliberately vulnerable, giving him a combination of strong energy drinks and preparing traps to entice him to her. However blunt she may be, Shido has not acknowledged or reciprocated her feelings.
Origami has also proven to value Shido's life over her loyalty to AST and DEM, going so far as to steal a dangerous CR-Unit from them and combat them specifically to protect him. However, she does not seem to value his emotions above her revenge, as while she does try to remove him physically from her fights with Kotori and the other spirits, she makes no attempt to stop or even consider his reaction to her killing them. This is especially evident in regards to Kotori, since she is Shido's sister, while Origami later admitted she didn't want to kill Kotori, and readily believed Shido when he said that it was a different spirit that killed her parents, it is clear that had Shido not told her that then she would have without regret.
Origami sees Tohka as an enemy, love rival, and an annoying "baka" that gets in her way with Shido. Origami shows little respect for her as the quarrel between them as Spirit and AST member remains unsettled despite the fact that Tohka's powers are sealed. Origami does not trust her very much as she views every other Spirit but is not hostile to her due to Tohka's currently sealed status.
In Volume 10, it is revealed that Origami actually began to get used to living with Tohka and the other spirits. Enraged by this, she decided to defeat Tohka and the other spirits once and for all and return her life to normal. During the battle, Origami was able to defeat Tohka, Miku, and the Yamai sisters in their limited release Astral Dress. However, just as Origami was about to finish them off, Tohka regained her full power and defeated her. After <Phantom> made Origami a spirit, she obtained many long-range abilities which made her a bad match for Tohka who mostly uses close-range abilities. During the battle between the two spirits, Tohka asked Origami if they could perhaps find a way to understand each other but Origami told her that she will reject all Spirits (despite the fact that she became one herself).