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There is renewed interest in the spectroscopy of heavy metal containing polar radical diatomic molecules because they provide a sensitive venue for detection of parity nonconservation (PNC) either from the determination of the electric dipole moment (EDM) {\textbf{56} } R3326, 1997.} of the electron, \textit{d}, or detection of the interaction of the anapole moment of the nuclei with the unpaired electron {\textbf{100}} 023003, 2008.}. The effects due to \textit{d} are nuclear spin independent and studies of both the even and odd nuclear spin isotopologues are relevant. Recently, DeMille \textit{et al} proposed using an odd isotopologue of barium monofluoride, $\mathrm{<mrow\; data-mjx-texclass="ORD">137</mrow>}BaF$, to measure the nuclear spin-dependent parity non-conservation (NSD-PNC) effect resulting from the interaction of the anapole moment of $\mathrm{<mrow\; data-mjx-texclass="ORD">137</mrow>}Ba$ with the unpaired electron of the $X2\Sigma +$ electronic state. Here we report on the analysis of the field-free spectrum of the $A2$$\Pi -X2\Sigma +$(0,0) band of $\mathrm{<mrow\; data-mjx-texclass="ORD">137</mrow>}BaF$ and an analysis of the $\mathrm{<mrow\; data-mjx-texclass="ORD">137</mrow>}Ba(I=3/2)$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">19</mrow>}F(I=1/2)$ hyperfine interaction in the $A2$$\Pi$ state. The hyperfine interaction in the $X2\Sigma +$ state has been previously characterized from the analysis of the pure rotation spectrum. {\textbf{71}} 389, 1982.} The optimal optical transitions for monitoring $\mathrm{<mrow\; data-mjx-texclass="ORD">137</mrow>}BaF$ in future PNC measurements will be discussed.