  We study the constraints on low-energy coefficients of the $\nu$SMEFT
generalization of the Standard Model effective theory in the simple case of a
$\text{U}(1)^\prime$ enlargement of the Standard Model gauge group. In
particular, we analyse the constraints imposed by the requirement that the
extended theory remains free of gauge anomalies. We present the cases of
explicit realisations, showing the obtained correlations among the coefficients
of $d=6$ operators.
