Step 1: In the case of degenerate orbitals (such as 2p\(_x\) and 2p\(_y\) orbitals in a hydrogen atom), transitions between them can occur and produce spectral lines. Hence, Statement I is correct.
Step 2: However, Statement II is incorrect. The 2p\(_x\) and 2p\(_y\) orbitals are not degenerate in a real atom due to the presence of the electric field of the atom (i.e., their energies are slightly different).
Thus, the correct answer is that Statement I is true and Statement II is false.