Concept:
Indian theatre and folk performance traditions can be classified according to their social, ritualistic, religious, and performative functions. Many forms evolved as temple traditions, ritual performances, or community entertainment.
Step 1: Match Koodiattam with its type.
\[
\text{Koodiattam}
\]
is an ancient Sanskrit theatre tradition performed in temple theatres and associated with:
\[
\text{Religious Form}
\]
Thus:
\[
A \rightarrow II
\]
Step 2: Match Naga Mandala with its type.
\[
\text{Naga Mandala}
\]
is connected with serpent worship rituals and belongs to:
\[
\text{Ritualistic Dance Form}
\]
Thus:
\[
B \rightarrow III
\]
Step 3: Match Kummi with its type.
\[
\text{Kummi}
\]
is a folk dance performed collectively by village communities and is a:
\[
\text{Community Dance}
\]
Thus:
\[
C \rightarrow I
\]
Step 4: Match Terukoothu with its type.
\[
\text{Terukoothu}
\]
is a Tamil folk theatre traditionally performed in open public spaces and streets.
Hence, it is a:
\[
\text{Street Form}
\]
Thus:
\[
D \rightarrow IV
\]
Step 5: Write the final matching sequence.
The correct matching is:
\[
A\text{-}II,\ B\text{-}III,\ C\text{-}I,\ D\text{-}IV
\]
Step 6: Compare with the given options.
Among the given choices:
\[
(A)\ A\text{-}I,\ B\text{-}II,\ C\text{-}IV,\ D\text{-}III
\]
\[
(B)\ A\text{-}III,\ B\text{-}II,\ C\text{-}IV,\ D\text{-}I
\]
\[
(C)\ A\text{-}II,\ B\text{-}III,\ C\text{-}I,\ D\text{-}IV
\]
\[
(D)\ A\text{-}IV,\ B\text{-}I,\ C\text{-}II,\ D\text{-}III
\]
the correct answer is:
\[
\boxed{A\text{-}II,\ B\text{-}III,\ C\text{-}I,\ D\text{-}IV}
\]
Hence:
\[
\boxed{\mathrm{(C)}}
\]