This paper adds to the discussion on the legal personhood of artificial intelligence by focusing on one area not covered by previous works on the subject – ownership of property. The author discusses the nexus between property ownership and legal personhood. The paper explains the prevailing misconceptions about the requirements of rights or duties in legal personhood, and discusses the potential for conferring rights or imposing obligations on weak and strong AI. While scholars have discussed AI owning real property and copyright, there has been limited discussion on the nexus of AI property ownership and legal personhood. The paper discusses the right to own property and the obligations of property ownership in nonhumans, and applying it to AI. The paper concludes that the law may grant property ownership and legal personhood to weak AI, but not to strong AI.