The reactions 3He(π+,pp)p and 3He(π-,pn)n were studied at 37.0 MeV by coincidence detection of two nucleons. The differential cross sections were separated to two-nucleon (σ2N), three-nucleon (σ3N), and final-state interaction (σFSI) components. For π+, the σ2N angular distribution is symmetric about 90°, and the total cross section is 1.5 times the cross section measured for d(π+,pp). For π-, the angular distribution is asymmetric (backward peaked). The asymmetry increases with decreasing energy, indicating increasing pion s-wave contribution at lower energies. The fraction of the cross section induced by s-wave pions as calculated by a partial wave amplitude analysis is 13%. The measured total cross sections are σ2N(π-)=0.85 ±0.08 mb and σ2N(π+)=7.9±0.5 mb; σ3N(π-)=1.6±0.7 mb and σ3N(π+)=1.3±0.3 mb. A new evaluation of σ3N, at Tπ=62.5 and 82.8 MeV is given, using data from an earlier experiment. The cross sections leading to the two-nucleon final-state interaction at Tπ=37.0 MeV are also estimated.