The authors present and prove a character sum analog of Selberg’s multidimensional beta function integral that is valid over any local completion field \(\mathbb{K}\) of \(\mathbb{Q}\) (\(\mathbb{K}\) is \(\mathbb{R}\) or a \(p\)-adic field \(\mathbb{Q}_ p\)) although if \(p=2\), it has only been proved for characters of rank less than 4: \[ \int {{dx} \over {| x(1-x)|}} \int {{dy} \over {| y(1-y)|}} \pi_ 1(xy)\pi_ 2((1-x)(1- y))\pi^ 2_ 3(x-y)= {\textstyle {1\over 2}} \sum_ \tau S(\pi_ 1,\pi_ 2,\pi_ 3,\pi_ \tau) \] where \[ S(\pi_ 1,\pi_ 2,\pi_ 3)= {{\Gamma(\pi_ 0 \pi_ 3^ 2) \Gamma(\pi_ 1)\Gamma(\pi_ 1,\pi_ 3)\Gamma(\pi_ 2)\Gamma (\pi_ 2\pi_ 3)} \over {\Gamma(\pi_ 0\pi_ 3) \Gamma(\pi_ 1\pi_ 2\pi_ 3) \Gamma(\pi_ 1\pi_ 2\pi_ 3^ 2)}} \] and \[ \Gamma(\pi)=\int_ \mathbb{K} {{dx} \over {| x|}}\chi(x)\pi(x). \] Here \(\chi(x)\) is an additive character, \(\pi_ 0(x)= | x|\), \(\pi_ i(x)\) are arbitrary multiplicative characters. The sum is over the quadratic classes of the number field with \(\pi_ \tau\) the corresponding local quadratic character.