Terre Haute is generally a safe city, but the same precautions for any other city apply here. Don't go out alone at night, don't flash money around and avoid the sections of town without streetlights, as crime tends to be higher there.
Although it is on the edge of Tornado Alley, Terre Haute does experience severe thunderstorms and the occasional tornado warning. Most of these occur in the spring and summer but there have been severe weather events in other months. There are sirens near Indiana State University, but they can only be heard within a mile of the campus. It is usually recommended to tune into local television or radio stations if there is a chance of severe weather.