Resulting from the Higgs mechanism of electroweak symmetry breaking in the standard model (SM) vector bosons (VB) gain mass and an additional degree of freedom in their possible polarization states. This third - longitudinal - polarization is inherently connected to the Higgs mechanism and opens the door for searches for possible new physics beyond the SM. A model independent approach to characterize deviations from the SM is Standard Model Effective Field Theory (SMEFT). It extends the SM by introducing higher dimension operators into the Lagrange density. This thesis studies W±Z production processes in a phase space sensitive to VB polarization in the light of possible sensitivity to SMEFT contributions. Eight dimension 6 operators are separately simulated with the help of the event generator SHERPA at leading order with fully leptonic decay channels. Their influence on multiple observables at current Wilson coefficient bounds is assessed. Even though further studies have to be conducted to better understand remaining issues connected to simulation of propagator contributions and closure between different contribution extraction approaches during the simulation of the SMEFT model, five of the eight studied operators show shape effect contributions in multiple observables. Fits of the operator contributions to the SM with basic binning led to tighter bounds on the Wilson coefficients of the O_φq3 and the O_W operators, suggesting sensitivity of the studied W^±Z polarization phase space to SMEFT contributions. Tighter bound setting of more operators seems to be possible if more sophisticated binning and bin optimization methods were applied in the future.