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By studying the spin structure of an S-wave meson-antimeson system in theheavy quark limit, we find two selection rules for the $c\bar{c}$ spin$J_{c\bar{c}}$ being only 1: (a) $J=min(J_\ell)-1$ or $J=max(J_\ell)+1$; (b)$J^C=1^+,2^-,3^+,\cdots$ if the two mesons are different but belong to the samedoublet. Here $J_\ell$ is the total angular momentum of the light degree offreedom. The rules may constrain decay channels of a meson-antimeson moleculeor resonance. For the recently observed $Z_c(3900)$ state, it in principle candecay into $J_{c\bar{c}}=0$ charmonium channels if it is a $D\bar{D}^*$molecule or resonance. The non-observation of $h_c\pi$ decay might imply thatthis state is a tetraquark.

Heavy quark spin selection rules in S-wave meson-antimeson states