The USS Carolina was a Federation starship that was in service during the mid-23rd century.
It was deployed to the sector near Capella IV in 2267, and apparently sent a distress signal to the USS Enterprise. However, the Enterprise had previously been diverted by a fake distress call from the SS Deirdre, and acting captain Montgomery Scott, while choosing to ignore the distress class, observed, "Fool me once, shame on you. Fool me twice, shame on me." (TOS: "Friday's Child")
Background
According to the Star Trek Encyclopedia, the Carolina was an old Daedalus-class starship with the registry number NCC-235. However, TNG: "Power Play" clearly states that all Daedalus-class ships were decommissioned by 2196, 71 years before "Friday's Child." Uhura spoke of the Carolina as a starship that appeared to be currently registered in the sector, not as an old, decommissioned vessel. Therefore, it is probable that the Carolina's status as a Daedalus-class ship is incorrect.
The Encyclopedia contradicts itself concerning the registry number as well, listing it as NCC-235 on page 66 of the second and third editions, while page 417 (the starship list) gives a registry of NCC-160.
While not an official source, Decipher role playing game supplement states that this vessel may be a Ranger-class starship
This ship is named after the Province of Carolina, a British colony in North America.