The general merit scholarships are awarded without application. The financial aid appears to be a blend of need + merit. Rose has a calculator on their site that provides an estimate of merit (and need-based) money you may receive:
https://www.rose-hulman.edu/admissions-and-aid/financial-aid/roi-form.html
If you play with the inputs a bit, you can see how the numbers change. As a single anecdote from last year, @locococomama posted a merit scholarship of $21,500, no submission of FAFSA.