Neutral kaon pairs produced in ϕ decays in anti-symmetric entangled state can be exploited to search for violation of CPT symmetry and Lorentz invariance. We present an analysis of the CP-violating process ϕ→KSKL→π+π−π+π− based on 1.7 fb−1 of data collected by the KLOE experiment at the Frascati ϕ-factory DAΦNE. The data are used to perform a measurement of the CPT-violating parameters Δaμ for neutral kaons in the context of the Standard Model Extension framework. The parameters measured in the reference frame of the fixed stars are: Δa0=(−6.0±7.7stat±3.1syst)×10−18 GeV, ΔaX=(0.9±1.5stat±0.6syst)×10−18 GeV, ΔaY=(−2.0±1.5stat±0.5syst)×10−18 GeV, ΔaZ=(3.1±1.7stat±0.5syst)×10−18 GeV. These are presently the most precise measurements in the quark sector of the Standard Model Extension.