In this paper, we use a reconfigurable intelligent surface (RIS) to enhance the radar sensing and communication capabilities of a mmWave dual function radar communication system. To simultaneously localize the target and to serve the user, we propose to adaptively partition the RIS by reserving separate RIS elements for sensing and communication. We design a multi-stage hierarchical codebook to localize the target while ensuring a strong communication link to the user. We also present a method to choose the number of times to transmit the same beam in each stage to achieve a desired target localization probability of error. The proposed algorithm typically requires fewer transmissions than an exhaustive search scheme to achieve a desired target localization probability of error. Furthermore, the average spectral efficiency of the user with the proposed algorithm is found to be comparable to that of a RIS-assisted MIMO communication system without sensing capabilities and is much better than that of traditional MIMO systems without RIS.

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