  We study the exotic $J^{PC}=0^{--}$ four-quark states in Laplace sum rules
(LSR) and finite energy sum rules (FESR). We use the vector tetraquark-like
currents as interpolating currents in the correlator, from which the $1^{+-}$
states are also studied. In the mass extraction, we use the standard stability
criterion with respect to the Borel parameters and the QCD continuum thresholds
and consider the effect of the violation of factorization in estimating the
high dimensional condensates as a source of uncertainties. The obtained mass
prediction $1.66\pm0.14$ GeV is much lower than the previous sum rule
predictions obtained using the scalar currents. Our result favours the
four-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$
decay. We also discuss the possible decay patterns of these exotic four-quark
states.
