She is Baki's girlfriend and her mother, Kinuyo Matsumoto, is Baki's landlord. She cares deeply for Baki, but denies when asked. She is disillusioned by Baki's violent life as an Underground fighter and begs him several times to quit. Though she still disapproves, Kozue better understands Baki's resolve after visiting Emi Akezawa's grave site. After Baki's first tournament match, he reveals that he cares for Kozue. She became his love interest in the second series, and makes love with him just before his fight with Yanagi Ryuukou, allowing Baki to become a "full man". It should also be noted that Yujiro Hanma views her as an excellent woman for Baki. Yujiro also states: "that little bastard got the best woman in the world", after she helped Baki cure the poison left by Ryuukou Yanagi.
Though she appears to have a passive and soft personality, she has no problem asserting herself. When Kaoru Hanayama approaches Baki while with Kozue and questions their relationship as an inhibiting factor of Baki's fighting progress and offering alternative situations for Baki to have sex outside of a committed relationship, Kozue firmly confronts Hanayama and scolds him for disrespecting their relationship. She criticizes how men overall prioritize fighting and competition so much that the women in their lives are entirely excluded from consideration as significant factors in their decisions or how they are affected by their dangerous way of life. She goes as far as lightly kicking his leg each time she makes a statement.
Moments before Baki fights Ryuukou Yanagi, she wants to help in the fighting. Despite not understanding the level of danger and skill Yanagi possessed, her supportive nature and her courage as his partner is constructive for Baki in the long term. She also steps between Baki and Yujiro while they were "flirting" during their fight, even scolding them for beating around the bush.