A bstract A measurement of the inclusive cross section of top quark pair production in association with a Z boson using proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC is performed. The data sample corresponds to an integrated luminosity of 77.5 fb − 1 , collected by the CMS experiment during 2016 and 2017. The measurement is performed using final states containing three or four charged leptons (electrons or muons), and the Z boson is detected through its decay to an oppositely charged lepton pair. The production cross section is measured to be σ ( $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mover><mml:mi>t</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>Z</mml:mi></mml:math> ) = 0 . 95 ± 0 . 05 (stat) ± 0 . 06 (syst) pb. For the first time, differential cross sections are measured as functions of the transverse momentum of the Z boson and the angular distribution of the negatively charged lepton from the Z boson decay. The most stringent direct limits to date on the anomalous couplings of the top quark to the Z boson are presented, including constraints on the Wilson coefficients in the framework of the standard model effective field theory.