Detailed magnetic field structure of the dense core SL42 ( CrA-E ) in the Corona Australis molecular cloud complex was investigated based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains . The magnetic fields in and around SL42 were mapped using 206 stars and curved magnetic fields were identified . On the basis of simple hourglass ( parabolic ) magnetic field modeling , the magnetic axis of the core on the plane of sky was estimated to be 40 ^ { \circ } \pm 3 ^ { \circ } . The plane-of-sky magnetic field strength of SL42 was found to be 22.4 \pm 13.9 \mu G. Taking into account the effects of thermal/turbulent pressure and the plane-of-sky magnetic field component , the critical mass of SL42 was obtained to be M _ { cr } = 21.2 \pm 6.6 M _ { \odot } , which is close to the observed core mass of M _ { core } \approx 20 M _ { \odot } . We thus conclude that SL42 is in a condition close to the critical state if the magnetic fields lie near the plane of the sky . Since there is a very low luminosity object ( VeLLO ) toward the center of SL42 , it is unlikely this core is in a highly subcritical condition ( i.e. , magnetic inclination angle significantly deviated from the plane of sky ) . The core probably started to collapse from a nearly kinematically critical state . In addition to the hourglass magnetic field modeling , the Inoue & Fukui ( 2013 ) mechanism may explain the origin of the curved magnetic fields in the SL42 region .