<p>A search for flavor-changing neutral currents in top-quark decays <inline-formula><mml:math display="inline"><mml:mi>t</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>Z</mml:mi><mml:mi>q</mml:mi></mml:math></inline-formula> is performed in events produced from the decay chain <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mo stretchy="false">→</mml:mo><mml:mi>Z</mml:mi><mml:mi>q</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mi>W</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>, where both vector bosons decay leptonically, producing a final state with three leptons (electrons or muons). A data set collected with the CMS detector at the LHC is used, corresponding to an integrated luminosity of <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>19.7</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:msup><mml:mrow><mml:mi>fb</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of proton-proton collisions at a center-of-mass energy of 8 TeV. No excess is seen in the observed number of events relative to the standard model prediction; thus, no evidence for flavor-changing neutral currents in top-quark decays is found. A combination with a previous search at 7 TeV excludes a <inline-formula><mml:math display="inline"><mml:mi>t</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>Z</mml:mi><mml:mi>q</mml:mi></mml:math></inline-formula> branching fraction greater than 0.05% at the 95% confidence level.</p>