A search is presented for narrow heavy resonances decaying to a top quark and a bottom quark using data collected by the CMS experiment at in 2016. The data set analyzed corresponds to an integrated luminosity of 35.9 . Final states that include a single lepton (e, μ), multiple jets, and missing transverse momentum are analyzed. No evidence is found for the production of a boson, and the production of right-handed bosons is excluded at 95% confidence level for masses up to 3.6 depending on the scenario considered. Exclusion limits for bosons are also presented as a function of their coupling strength to left- and right-handed fermions. These limits on a boson decaying via a top and a bottom quark are the most stringent published to date.