This article integrates rate-splitting multiple access (RSMA) and hybrid beamforming (HB) with cell-free massive multiple-input multiple-output (CF-mMIMO) network to enhance both spectral efficiency (SE) and energy efficiency (EE). RSMA, which provides both common message service and private message service, has been shown to outperform space-division multiple access (SDMA) in a wide range of network deployments. In previous studies employing RSMA for CF-mMIMO network, all access points (APs) were assumed to provide common message service. However, with the RF chain limitation in the HB architecture, APs can not provide all services and therefore AP-service association is essential. To handle it, we first propose to design the analog beamformers in a heuristic manner. Then an optimization problem for the maximization of the tradeoff between SE and EE, where digital precoders and AP-service association are jointly considered, is formulated and finally transformed into a tractable second-order cone programming (SOCP) one. Numerical results validate the superiority of RSMA with AP-service association over SDMA and RSMA without AP-service association in both SE and EE.