55Mn nuclear magnetic resonance experiments are reported on a series of fully strained epitaxial La(2/3)Ca(1/3)MnO3 thin films on SrTiO3. We have found evidence of multiple phase segregation into ferromagnetic metallic and nonmetallic regions as well as regions that are nonferromagnetic and insulating. These insulating regions are mainly located close to interfaces and may have a significant impact on the performance of spin-tunnel devices. As a result of phase segregation, the ferromagnetic coupling within the metallic regions is depressed. This accounts for the reduction of the Curie temperature and conductivity in nanometric thin films.