Answer: Yes, you can definitely do that. There are two departure points for the Statue of Liberty ferry, both operated by City Cruises, which is the only official company authorized to take visitors to the Statue of Liberty and Liberty Island. The ferry ticket to the Statue of Liberty is a round trip ticket that allows you to choose between two departure points:
According to City Cruises’ policy on the company’s official website, there is no restriction that prevents you from taking the outbound ferry from one side and returning on the ferry to the other side. You are completely free to do so without any issue.
