Coarea formula for functions on 2-step Carnot groups with sub-Lorentzian structure

We consider $C^1$-functions defined on two-step Carnot groups with a sub-Lorentzian structure defined by one horizontal direction with a negative squared length along it, and prove a nonholonomic coarea formula. A result of interest in itself concerns the correctness of the problem statement, namely, the level sets have to be spacelike.