The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent ν is topologically invariant and equal to the self-avoiding walk value (in the present case ν=3/4), and that the topology and dimensionality of the system strongly influence the crossover between the rigid regime and the self-avoiding regime at a scale L≈7ℓp. Additionally, the bond correlation function scales with the molecular length L as predicted. For molecular lengths L≤5ℓp, circular DNA behaves like a stiff molecule with an approximately elliptic shape.