Conformal phased arrays can be found in many applications due to their ability to fit tridimensional surfaces and, thanks to their scanning performance, can excel planar arrays. However, most of the previously proposed analysis methods can be applied only to canonical cases and do not consider the effects of polarization. Therefore, this paper presents a closed-form formulation for analyzing antenna arrays conformal to arbitrary surfaces, evaluating the effects of the polarization components on the overall radiation performance. Besides, an on-body array conformal to the human torso surface is analyzed as a case study, and its beam scanning performance is evaluated with the developed in-house code. Finally, an amplitude tapering methodology is proposed to switch off shadowed elements and redistribute the power to the operational ones. After applying this tapering strategy, the results show that the maximum directivity is maintained, and a significant reduction in the side lobe levels is achieved.