The structures and the thermodynamic properties of a fluid composed of a nonpolar or a polar dumbbell molecule have been studied from the gaslike to the liquidlike density regions based on two types of the reference interaction site model (RISM) integral equation theories (RISM-1 and RISM-2). This is the first application of the RISM-2 theory to a polar dumbbell fluid. We have proven that the RISM-2 theory with the hypernetted-chain (HNC) approximation has an inconsistency with respect to the zeroth-order relation between site-site total correlation functions and site-site direct correlation functions in the Fourier space, An hypothetical bridge function is introduced to remedy this inconsistency, which works well to give good information on the structure and the dielectric constant in the lower-density region. On the other hand, the RISM-1 theory works well in the higher-density region, but not well in the lower-density region. Complemental application of these theories, that is, the RISM-1 theory for the high-density region and the RISM-2 theory for the low-density region, allows us to understand the properties of fluid over wide density regions.