The low spin rates measured for solar-type stars at an age of a few Myr (~10% of the break-up velocity) indicate that some mechanism of angular momentum regulation must be at play in the early pre-main sequence. We characterize the rotation properties for members of the region NGC 2264 (~3 Myr), and investigate the accretion-rotation connection at an age where about 50% of the stars have already lost their disks. We examined a sample of 500 cluster members whose photometric variations were monitored in the optical for 38 consecutive days with CoRoT. Light curves were analyzed for periodicity using the Lomb-Scargle periodogram, the autocorrelation function and the string-length method. The period distribution obtained for the cluster consists of a smooth distribution centered around P=5.2 d with two peaks at P=1-2 d and 3-4 d. A separate analysis of CTTS and WTTS indicates that the P=1-2 d peak is associated with the latter, while both groups contribute to the P=3-4 d peak. The comparison between CTTS and WTTS supports the idea of a rotation-accretion connection: their respective rotational properties are statistically different, and CTTS rotate on average more slowly than WTTS. We also observe a clear dearth of fast rotators with strong accretion signatures (large UV flux excess). This is consistent with earlier findings that fast rotators in young star clusters are typically devoid of dusty disks. Our sample shows some evidence of a mass dependence in the rotation properties of NGC 2264 members, lower-mass stars spinning on average faster. This study confirms that disks influence the rotational evolution of young stars. The idea of disk-locking may be consistent with the picture of rotation and rotation-accretion connection that we observe for the NGC 2264 cluster. However, the origin of the several substructures that we observe in the period distribution deserves further investigation.
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