Step 1: Identify the hybridization of carbon bonded to oxygen.
In
\[
\text{t-Butyl alcohol } \left((\mathrm{CH_3})_3\mathrm{COH}\right),
\]
the carbon attached to the hydroxyl group forms four single bonds.
Hence, it is
\[
\boxed{sp^3\text{-hybridized}.}
\]
Step 2: Examine the remaining compounds.
In formic acid, urea and acetaldehyde, the carbon bonded to oxygen is part of a carbonyl group
\[
(\mathrm{C=O}),
\]
which is
\[
\boxed{sp^2\text{-hybridized}.}
\]
Therefore, these compounds do not satisfy the condition.
Step 3: Choose the correct option.
Hence,
\[
\boxed{\text{t-Butyl alcohol}}
\]
is the correct answer.
Therefore, the correct option is \(\boxed{(C)}\).