We study the singularities of solutions in 𝙱𝙼𝙾ᵠ ̛ ᵖ of an complex vector field L= X + iY. Necessary and sufficient conditions are established in the plane when ℋ𝜑(Σ) = 0, where Σ is the set where X, Y are linearly dependent and ℋ𝜑 is the Hausdorff measure defined by 𝜑.