None at present. The 1967 Outer Space Treaty prohibits nuclear weapons in space, but does not restrict peaceful uses of nuclear energy. A Mars base that is deve

None at present. The 1967 Outer Space Treaty prohibits nuclear weapons in space, but does not restrict peaceful uses of nuclear energy. A Mars base that is developed enough not only to support permanent human habitation but to conduct nuclear rocketry R&D is so far from where we are now that I couldn't speculate about what sort of laws might then apply on Mars, though.