Hiro placed an order for her shortly after Mao came to stay with him. One reason Hiro bought Croquette was so that Mao wouldn't be so lonely and so that she could have company. Croquette lives indoors and shares her residence with Hiro, Mao, Daiki and Wakaba and sleeps in the living room. For breakfast, she eats dog food soaked in milk. Being a dog, she is shown more often in the manga than Wakaba as she spends time with the family outside their home as well. Her name was suggested by Hiro and derived from the online novel authored by Mao of a dog with the same name.
Croquette is shown to have a rather inquisitive and playful personality but is also fairly obedient as shown when she and Mao waited outside for Hiro to come back or when Hiro brought her to the crowded night market. She is often seen in the arms of one of the three members of the Nakamura household but actually hates being picked up or kissed, even so, she usually tolerates the cuddling. 
Hiro happens to be Croquettes favourite human and he loves Croquette a lot. He had always wanted a dog but did not have time to look after one as a dog requires a fair bit of attention and looking after. After Mao came to live with him he decided they would be able to split their time caring for the dog. Hiro can often be seen babying Croquette in his arms or talking to her. While browsing through the night market, he buys her a nice sash that goes over her collar.
Mao was surprised when she came home to see a little puppy waiting at the door with Hiro. She loves Croquette very much and looks after her as well as take her on walks voluntarily. She also buys accessories for Croquette as seen when she buys a collar with an odd two-headed character sewn onto it. Croquette likes these weird toys that Mao gives her, but she does not like being kissed by Mao. She often asks for the opinion of and holds strategy meetings with Wakaba and Croquette.
Daiki likes Croquette a lot and first heard of her from Daiki. He can be seen playing with her and carrying her occasionally. Croquette mentions that Daiki usually cares for her when they are alone together, and appreciates how Daiki leaves Croquette alone (since Croquette dislikes being cuddled).
When Hina first sees Croquette during the family trip in Sendai, she is asked by Mao's younger sister Yui if Hina wants to try holding Croquette. Croquette initially rejects her, but she eventually is able to hold and cuddle Croquette.