  We provide a characterization of the crystal bases for the quantum queer
superalgebra recently introduced by Grantcharov et al.. This characterization
is a combination of local queer axioms generalizing Stembridge's local axioms
for crystal bases for simply-laced root systems, which were recently introduced
by Assaf and Oguz, with further axioms and a new graph $G$ characterizing the
relations of the type $A$ components of the queer crystal. We provide a
counterexample to Assaf's and Oguz' conjecture that the local queer axioms
uniquely characterize the queer supercrystal. We obtain a combinatorial
description of the graph $G$ on the type $A$ components by providing explicit
combinatorial rules for the odd queer operators on certain highest weight
elements.
