Despite long-standing interest and a vast body of literature, there is still disagreement as to how handedness should be measured in nonhuman primates. The primary goal of this study was to evaluate two common measures of handedness in nonhuman primates using the spider monkey, a unique study species due to its lack of a thumb and limited dexterity. Contrary to our predictions and previous findings in Ateles, there was no evidence for group-level hand biases on either the coordinated bimanual TUBE task or a unimanual reaching task. At the individual level, monkeys exhibited preferences on both tasks. There was a leftward trend on the bimanual task and a rightward trend on the unimanual task. Monkeys that were strongly lateralized on the bimanual task showed a comparable hand preference on the unimanual task, whereas monkeys with a moderate preference on the bimanual task shifted to the opposite hand on the unimanual task. Comparing across measures, the two hand-use patterns reported (consistent and shift) might have obscured group-level findings, given the available sample size. Overall, these data reaffirm that task type influences hand use in primates, and multiple measures are needed to fully characterize the construct of handedness. Consideration should be given to the difficulty required between tasks as well as between species.