  Given an imaginary quadratic number field $K$ with ring of integers
$\mathcal{O}_K$, we are interested in the asymptotic \emph{distance to nearest
neighbour} (or \emph{gap}) statistic of complex Farey fractions $\frac{p}{q}$,
with $p,q \in \mathcal{O}_K$ and $0<|q|\leq T$, as $T \to \infty$.
Reformulating this problem in a homogeneous dynamical setting, we follow the
approach of J. Marklof for real Farey fractions with several variables (2013)
and adapt a joint equidistribution result in the real $3$-dimensional
hyperbolic space of J. Parkkonen and F. Paulin (2023) to derive the existence
of a probability measure describing this asymptotic gap statistic. We obtain an
integral formula for the associated cumulative distribution function, and use
geometric arguments to find an explicit estimate for its tail distribution in
the cases of Gaussian and Eisenstein fractions.
