Single crystals of CaFe2(As1-xPx)(2) are found to exhibit the tetragonal (T) to collapsed-tetragonal (cT) transition at T-cT less than or similar to 100 K for x > 0.05. The c-axis shrinks by similar to 9% below T-cT, which substantially diminishes the interband nesting between the hole and electron bands. In sharp contrast to the superconducting T phase of AFe(2)(As1-xPx)(2) (A = Ba, Sr), where the anomalous non-Fermi liquid transport properties are observed, the resistivity, Hall coefficient, and magnetoresistance data in the Ca-based system all indicate that the standard Fermi liquid behaviors are recovered abruptly below T-cT, and the superconductivity disappears completely. The simultaneous disappearance of the superconductivity and the non-Fermi liquid transport enlightens the essential role of interband-associated fluctuations to the superconductivity in Fe pnictides.