Methods of optimal laser control are developed to distinguish between pre-oriented molecules possessing a mirror-type symmetry and selectively prepare diatomic dissociation fragments rotating clockwise and anticlockwise by linearly polarized and shaped infrared (IR)-laser pulses of a picosecond (ps) duration. Quantum dynamical simulations performed for a three-dimensional (3D) model of HONO2 in the ground electronic state based on ab initio defined potential-energy surface and dipole function show that the ON single bond can be broken with almost 100'% probability and the OH fragments rotating clockwise, OH(c), and anticlockwise, OH(a), can be selectively prepared, with the branching ratio being as high as 25.14 for isolated molecules and as high as 12.47 for the gas phase thermal ensembles at T < 1 K.