Grasping is a highly complex movement that requires the coordination of a number of hand joints and muscles. Previous studies showed that spinal premotor interneurons (PreM-INs) in the primate cervical spinal cord have divergent synaptic effects on hand motoneurons and that they might contribute to hand-muscle synergies. However, the extent to which these PreM-IN synaptic connections functionally contribute to modulating hand-muscle activity is not clear. In this paper, we explored the contribution of spinal PreM-INs to hand-muscle activation by quantifying the synaptic linkage (SL) and functional linkage (FL) of the PreM-INs with hand-muscle activities. The activity of 23 PreM-INs was recorded from the cervical spinal cord (C6-T1), with EMG signals measured simultaneously from hand and arm muscles in two macaque monkeys performing a precision grip task. Spike-triggered averages (STAs) of rectified EMGs were compiled for 456 neuron-muscle pairs; 63 pairs showed significant post-spike effects (PSEs; i.e., SL). Conversely, 231 of 456 pairs showed significant cross-correlations between the IN firing rate and rectified EMG (i.e., FL). Importantly, a greater proportion of the neuron-muscle pairs with SL showed FL (43/63 pairs, 68%) compared with the pairs without SL (203/393, 52%), and the presence of SL was significantly associated with that of FL. However, a significant number of pairs had SL without FL (SL∩!FL, n = 20) or FL without SL (!SL∩FL, n = 203), and the proportions of these incongruities exceeded the number expected by chance. These results suggested that spinal PreM-INs function to significantly modulate hand-muscle activity during precision grip, but the contribution of other neural structures is also needed to recruit an adequate combination of hand-muscle motoneurons.