  Let $G=(V,\overrightarrow{E})$ be a graph with some prescribed orientation
for the edges and $\Gamma$ be an arbitrary group. If $f\in
\mathrm{Inv}(\Gamma)$ be an anti-involution then the skew gain graph
$\Phi_f=(G,\Gamma,\varphi,f)$ is such that the skew gain function
$\varphi:\overrightarrow{E}\rightarrow \Gamma$ satisfies
$\varphi(\overrightarrow{vu})=f(\varphi(\overrightarrow{uv}))$. In this paper,
we study two different types, Laplacian and $g$-Laplacian matrices for a skew
gain graph where the skew gains are taken from the multiplicative group
$F^\times$ of a field $F$ of characteristic zero. Defining incidence matrix, we
also prove the matrix tree theorem for skew gain graphs in the case of the
$g$-Laplacian matrix.
