CPS units are arranged by county and their standard way is to work within their home county with fostercare and adoptions (it's extra work on their part to go outside their county and have to work with another county, and the other counties have their own work to do so it's extra work for them, too). However, if there's a reason, they'll certainly work with other counties. For example, if no appropriate placement is available in their county. Sometimes they prefer placing a child out of the county, for the child's safety. For example, if criminal proceedings are going on against the parents or the parents aren't trusted not to harass the foster parents, or for some other reason it would be a terrible idea for the child and parent to run into each other. Another reason would be if a relative in another county, state, or even country agrees to take the child in and checks out okay. Then, say that placement disrupts (which in not uncommon). If the case has been transferred to the child's new county of residence, it's possible the child would return to care in the new county.
For story purposes, I think you could probably just have it happen and not bother with learning all the technicalities, it's likely enough to have reasons to occur that I doubt any reader would screech "It doesn't go that way!" Because, as above, it certainly could go that way. I could easily see reading a story where the child is then sent to another city and all that would be mentioned would be maybe a scene where the placement disrupts, with no explanation of CPS's behind-the-scenes decision-making.
Also, a note on another post below. In the US the term "group home" is used, not "orphanage." Plenty of people call them that anyway, informally, but just so you don't get a reader yelling that that's incorrect. And yes, teenagers are hard to place and most often do go to group homes although they'd be sent to a regular family home if one was available.
Another thing, for authenticity sake, foster parents and group homes need special training and certification (and get my remuneration) for kids who need higher levels of care than just more or less basic parenting. Those homes are fewer in number so that's another reason a child might be sent out of their home county for a placement. Serious medical needs and psychological needs or behavior problems, for example.