  A determination of the $C\!P$-even fraction $F_+$ in the decay $D^0 \to
K^+K^-\pi^+\pi^-$ is presented. Using $2.93$ fb$^{-1}$ of
$e^+e^-\to\psi(3770)\to D\bar{D}$ data collected by the BESIII detector, one
charm meson is reconstructed in the signal mode and the other in a $C\!P$
eigenstate or the decay $D\to K_{S, L}^0\pi^+\pi^-$. Analysis of the relative
rates of these double-tagged events yields the result $F_+ = 0.730 \pm 0.037
\pm 0.021$, where the first uncertainty is statistical and the second is
systematic. This is the first model-independent measurement of $F_+$ in $D^0
\to K^+K^-\pi^+\pi^-$ decays.
