The light vector mesons (ρ,ω, and ϕ) were produced in deuterium, carbon, titanium, and iron targets in a search for possible in-medium modifications to the properties of the ρ meson at normal nuclear densities and zero temperature. The vector mesons were detected with the CEBAF Large Acceptance Spectrometer (CLAS) via their decays to e+e−. The rare leptonic decay was chosen to reduce final-state interactions. A combinatorial background was subtracted from the invariant mass spectra using a well-established event-mixing technique. The ρ-meson mass spectrum was extracted after the ω and ϕ signals were removed in a nearly model-independent way. Comparisons were made between the ρ mass spectra from the heavy targets (A>2) with the mass spectrum extracted from the deuterium target. With respect to the ρ-meson mass, we obtain a small shift compatible with zero. Also, we measure widths consistent with standard nuclear many-body effects such as collisional broadening and Fermi motion.