  A general search is presented for a low-mass $\tau^-\tau^+$ resonance
produced in association with a bottom quark. The search is based on
proton-proton collision data at a center-of-mass energy of 13 TeV collected by
the CMS experiment at the LHC, corresponding to an integrated luminosity of
35.9 fb$^{-1}$. The data are consistent with the standard model expectation.
Upper limits at 95% confidence level on the cross section times branching
fraction are determined for two signal models: a light pseudoscalar Higgs boson
decaying to a pair of $\tau$ leptons produced in association with bottom
quarks, and a low-mass boson X decaying to a $\tau$-lepton pair that is
produced in the decay of a bottom-like quark B such that B $\to$ bX. Masses
between 25 and 70 GeV are probed for the light pseudoscalar boson with upper
limits ranging from 250 to 44 pb. Upper limits from 20 to 0.3 pb are set on B
masses between 170 and 450 GeV for X boson masses between 20 and 70 GeV.
