Approximately 90% of the human population is right-handed. The emergence of this hand preference in humans is thought to be linked to the ability to execute complex tasks and habitual bipedalism. In order to test these hypotheses, the present study explored, for the first time, hand preference in relation to both body posture (seated and bipedal) and task complexity (bimanual coordination and two tool use tasks of different complexity) in bonobos (Pan paniscus). Few studies have explored the effects of both posture and task complexity on handedness, and investigations with bonobos are scarce, particularly studies on tool use. Our study aims to overcome such a gap by addressing two main questions: 1) Does a bipedal posture increase the strength of hand preference and/or create a directional bias to the use of the right hand? 2) Independent of body posture, does task complexity increase the strength of the hand preference and/or create a directional bias to the use of the right hand? Our results show that independent of body posture, the more complex the task, the more lateralization occurred. Moreover, subjects tended to be right-handed for tasks involving tool use. However, posture had no significant effect on hand preference in the tasks tested here. Therefore, for a given task, bonobos were not more lateralized in a bipedal posture than in a seated one. Task complexity might thus have contributed more than bipedal posture to the emergence of human lateralization and the preponderance of right-handedness, although a larger sample size and more data are needed to be conclusive.