I believe most hotels, especially the larger chains, don't want suicides reported to avoid negative publicity and to discourage copy cats. I am somewhat thinking of CTBing in Las Vegas. I've researched it's estimated there are hundreds or possibly thousands of hotel suicides there each year but we never hear this in the news. In fact, they request that coroners and "clean up" companies use unmarked cars when dealing with suicides.
if you're from a small town area and CTB in another small town, there could be talk and gossip. I grew up in very small rural area where everyone knows everyone's business.
That said, if your suicide is, what's the word, uneventful, then it likely won't make the news. You know your region though. Have you seen suicides reported in the news? If not, I feel you'll be ok.
Oh one other thing. Based on my research, it sometimes appears questionable when a local resident checks into a hotel. You said you're going to a nearby town. I'd have a story prepared you might casually drop to avoid suspicion. If I CTB locally at a hotel I'd say my apartment is being painted so I need to move out for a couple days. Someone posted here last week she told the hotel she just needed some time away from her boyfriend. And you can request no room service, say you want to rest undisturbed. Or I was going to say I have a bunch of Skype work calls and don't want to be disturbed.