Analyze Statement (I): Aqueous solution of ammonium carbonate is basic.

Ammonium carbonate is $(NH_4)_2CO_3$ It is a salt of:

• weak base: $NH_4OH$ (or ammonia in water)
• weak acid: $H_2CO_3$

For salts of weak acid and weak base, the nature of the solution depends on comparison of hydrolysis tendencies, i.e. on $K_a$ and $K_b$.

Here:

• $NH_4^+$ is acidic
• $CO_3^{2-}$ is strongly basic

Also, carbonic acid is a weak acid, so its conjugate base $CO_3^{2-}$ has appreciable basic character. This basicity dominates over the acidity of $NH_4^+$.

Hence, aqueous ammonium carbonate solution is basic.

So, Statement (I) is correct.

Analyze Statement (II): Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $K_a$ and $K_b$ value of acid and the base forming it.

This is a standard result of salt hydrolysis.

For a salt formed from a weak acid and a weak base:

• if $K_b > K_a$, solution is basic
• if $K_a > K_b$, solution is acidic
• if $K_a = K_b$, solution is approximately neutral

Therefore, the acidic/basic nature indeed depends on the relative values of $K_a$ and $K_b$.

So, Statement (II) is correct.

Conclusion:

Both statements are correct.

Therefore, the correct option is: $\boxed{A}$