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We derive the covariant Poisson's equation of $(d+1)$-dimensional Newton-Cartan gravity with (twistless) torsion by applying the `non-relativistic conformal method' introduced in \cite{Afshar:2015aku}. We apply this method on-shell to a Schr\"odinger field theory on the curved Newton-Hooke background. The covariance of the field equation in the presence of the non-relativistic cosmological constant, entails fixing all coefficients in the covariant Poisson's equation for (twistless) torsional Newton-Cartan gravity. We further derive Ehlers conditions and an equation associated to the torsion in this method.
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