The present study employs the non-polynomial shear deformation theory within the framework of isogeometric analysis to study the vibration and buckling behavior of carbon nanotubes reinforced composite plates. Owing to the higher aspect ratio of carbon nanotubes, they are prone to agglomeration in matrix. Therefore, to analyze the effect of carbon nanotubes agglomeration in composite plates, a two-parameter micromechanics model is used to determine the effective mechanical properties of the composite plate. Current study opts isogeometric analysis as numerical method, as it can represents the complex shape geometries, and provides higher-order element continuity. Higher-order element continuity is desirable for implementation of non-polynomial shear deformation theory. By the virtue of non-uniform rational B-splines, isogeometric analysis turns out to be better analysis numerical method for complex and shell structures. Governing isogeometric element equations are derived using Hamilton's principle. A detailed parametric study is also performed to investigate the effect of degree of agglomeration, thickness to length/radius ratio, different boundary conditions, and complex shape cutouts in a composite plate. The presented formulation is validated across analytical and finite element method solutions with available literature.