We report observations from an experiment we carried out in the North Sea, close to the island of Helgoland in the summer of 2014. A commercial fibre-optic gyro (usually used for navigation purposes) recording ground rotation rate with a sensitivity of approx. 10^-7 rad/s was mounted on an OBS system together with a broadband seismometer. The system was lowered to the seafloor for about a week. To investigate a potential connection between rotational ground motions around the two horizontal axes (i.e., tilting) we calculate the coherence between the corresponding motion components (e.g., rotations around x-axis and translational motions along y-axis, and vice versa). We find very high correlations, on average exceeding 0.73 in the period interval 7-13 seconds. Correlations seem to increase with noise amplitude. Rotation rate amplitudes are in the range of 10^-6 -10^-5 rad/s. This clearly indicates that the horizontal translational components are severely contaminated by rotations around the horizontal axes. We investigate the origin of these rotational motions and correlate with wave height, wind information, and other parameters. In principle, the ground rotation observations allow correcting for the cross-coupling effect thereby improving the S/N on the horizontal translational components. We quantify the improvement of this procedure and discuss general requirements for broadband rotation sensors for OBS applications.