The magnetic field structure of a star-forming Bok globule BHR 71 was determined based on near-infrared polarimetric observations of background stars. The magnetic field in BHR 71 was mapped from 25 stars. By using a simple 2D parabolic function, the plane-of-sky magnetic axis of the core was found to be $theta_{rm mag} = 125^{circ} pm 11^{circ}$. The plane-of-sky mean magnetic field strength of BHR 71 was found to be $B_{rm pos} = 8.8 - 15.0$ $mu$G, indicating that the BHR 71 core is magnetically supercritical with $lambda = 1.44 - 2.43$. Taking into account the effect of thermal/turbulent pressure and the plane-of-sky magnetic field component, the critical mass of BHR 71 was $M_{rm cr} = 14.5-18.7$ M$_{odot}$, which is consistent with the observed core mass of $M_{rm core} approx 14.7$ M$_{odot}$ (Yang et al. 2017). We conclude that BHR 71 is in a condition close to a kinematically critical state, and the magnetic field direction lies close to the plane of sky. Since BHR 71 is a star-forming core, a significantly subcritical condition (i.e., the magnetic field direction deviating from the plane of sky) is unlikely, and collapsed from a condition close to a kinematically critical state. There are two possible scenarios to explain the curved magnetic fields of BHR 71, one is an hourglass-like field structure due to mass accumulation and the other is the Inoue & Fukui (2013) mechanism, which proposes the interaction of the core with a shock wave to create curved magnetic fields wrapping around the core.
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