We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying H\"ormander bracket condition. We deduce a unique continuation property for the square root of subelliptic Laplace operators under an additional analyticity condition. Then, with a different, more involved method, we prove the same result of unique continuation for more general $s$-powers ($0Comment: Content improved to include fractional powers. Consequently title changed
