We consider two dimensional Grushin Schrödinger equation posed on a finite cylinder Ω = (−1, 1) x × T y with Dirichlet boundary condition. We obtain the sharp observability by any horizontal strip, with the optimal time T * > 0 depending on the size of the strip. Consequently , we prove the exact controllability for Grushin Schrödinger equation. By exploiting the concentration of eigenfunctions of harmonic oscillator at x = 0, we also show that the observability fails for any T ≤ T * .