Let $G=(V,\overrightarrow{E})$ be a graph with some prescribed orientation for the edges and $Γ$ be an arbitrary group. If $f\in \mathrm{Inv}(Γ)$ be an anti-involution then the skew gain graph $Φ_f=(G,Γ,\varphi,f)$ is such that the skew gain function $\varphi:\overrightarrow{E}\rightarrow Γ$ 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.