She has been to the firehouse twice, and was the ex-girlfriend of Otis - having shown romantic feelings towards him when she came to the firehouse. They ended up kissing and playing Catan together.
Even though Kelly was her half brother, they only knew this in Season 2. They didn't recognise each other, and so Kelly thought Katie was dating Benny - however, in fact Katie was Benny's daughter, and Kelly's half sister.
They didn't have the perfect relationship, however Kelly tried to fix it, by inviting her to the firehouse to cook a few meals for the members. She rejected him at first but eventually accepted his invitation to visit 51.
She came around often and Kelly was visibly very protective of her since they met - including being closer to Katie than her own mother. Katie's mom was always occupied with her twin sons, which was shown when he was the only person to show up to her culinary graduation.
Katie gets kidnapped at the end of "Tonight's the Night" by Vince Keller's thugs (the person Kelly had stopped in the firehouse earlier that night, after Keller tried to kill someone). Kelly never gives up trying to find her, and with the help of Lindsay he does. He's very annoyed to see his sister like this: upset and beaten, after being raped by Keller. Keller later disappears, although it is hinted that Kelly "took care of him", and that he was never coming back.
She leaves after her attack after accepting the job offer from her boss in New York.