3-SAT where variables occur equally many times as a positive literal and as a negative literal

Question

Let $\phi$ be a 3-CNF formula over variables $x_1,x_2,\ldots,x_n$. Every variable $x_i$, $i \in [n]$, occurs equally many times as a positive literal and as a negative literal in $\phi$.

Is it NP-complete to decide the satisfiability of such a formula? Assuming it is, I would be interested in knowing if it has a special name. Has it perhaps also been investigated somewhere?