Step 1: Use diagonals:
Midpoint of AC: $\left(\tfrac{-2+3}{2}, \tfrac{-1+3}{2}\right) = (0.5, 1)$. Midpoint of BD: $\left(\tfrac{4-3}{2}, \tfrac{0+2}{2}\right) = (0.5, 1)$. Diagonals bisect each other, so ABCD is a parallelogram.
Step 2: Test further:
Diagonal lengths: $AC = \sqrt{25+16} = \sqrt{41}$ and $BD = \sqrt{49+4} = \sqrt{53}$. They differ, so it is not a rectangle.
Step 3: Check rhombus:
Diagonals $\overrightarrow{AC} = (5,4)$ and $\overrightarrow{BD} = (-7,2)$ have dot product $-35 + 8 = -27 \neq 0$, so they are not perpendicular, and it is not a rhombus. Option (A).
Final Answer:
It is a parallelogram only.
\[ \boxed{\text{(A) }\text{Parallelogram, not rhombus or rectangle}} \]