Step 1: Understanding the Concept
The inner ear has two functions: hearing, done by the cochlea, and balance, done by the vestibular apparatus.
Step 2: Statement (I)
The organ of Corti lies on the basilar membrane, but its hair cells are receptors for hearing and not for equilibrium. Statement (I) is incorrect.
Step 3: Statement (II)
The three semicircular canals, with the utricle and saccule, detect head movement and help maintain balance and posture. Statement (II) is correct.
Final Answer:
Statement (I) is incorrect but Statement (II) is correct.
\[ \boxed{\text{(D) }\text{Statement (I) is incorrect but Statement (II) is correct}} \]