Complete constraint analysis and choice of gauge conditions consistent with
equations of motion is done for Abelian Chern-Simons field interacting min
imally with a complex scalar field. The Dirac-Schwinger consistency conditi
on is satisfied by the reduced phase space Hamiltonian density with respect
to the Dirac bracket. It is shown that relativistic invariance under boost
s can be obtained only if gauge conditions were chosen consistent with the
equations of motion. Moreover all gauge-invariant quantities are shown to b
e free of transformation anomaly.