  A search is presented for a singly produced third-generation scalar
leptoquark decaying to a $\tau$ lepton and a bottom quark. Associated
production of a leptoquark and a $\tau$ lepton is considered, leading to a
final state with a bottom quark and two $\tau$ leptons. The search uses
proton-proton collision data at a center-of-mass energy of 13 TeV recorded with
the CMS detector, corresponding to an integrated luminosity of 35.9 fb$^{-1}$.
Upper limits are set at 95% confidence level on the production cross section of
the third-generation scalar leptoquarks as a function of their mass. From a
comparison of the results with the theoretical predictions, a third-generation
scalar leptoquark decaying to a $\tau$ lepton and a bottom quark, assuming unit
Yukawa coupling ($\lambda$), is excluded for masses below 740 GeV. Limits are
also set on $\lambda$ of the hypothesized leptoquark as a function of its mass.
Above $\lambda =$ 1.4, this result provides the best upper limit on the mass of
a third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom
quark.
