Unless it has been hung to dry under controlled circumstances, yes, it should be refrigerated. And of course, once it's cut, it MUST be refrigerated. Even under refrigeration, whole or cut, it won't keep forever.
Suzanne's point is well made yet to expand on this.......
It can be stored at cool temps (not under refrigeration like in a cellar) or even room temp (not above 95 for prolonged periods) if submersed in oil or lard. Curing can also be done outside of refrigeration.
Case in point.....my grandmother would cure her sausage under the back porch starting in October (Southside of Chicago....Roseland) and then place the cured sausages in stoneware crocks, and cover with cooled, melted pork lard. I have personally seen the sausage stored in the cellar for up to 2 years this way. Come to think of it.......I actually have 3 of those crocks in the shed today......unfortunately, very empty.
Anyhow, I have taken it a step further when doing my sausages and have sealed the cured product in Foodsaver bags with olive oil. I have stored them at room temp for up to a year with no issues. However, I have tried the process without the oil and it seemed to pick-up an off flavor. No one ever got sick (made 15lbs for 10 family and friends for first attempt) and the "off flavor" wasn't that strong but it was made me conscious enough to change the process.
But as always....when in doubt, refrigerate:thumb: