Having trouble to tell what kind of filter (Low-Pass, High-Pass,
Band-Pass, Band-Reject(Notch) are present given a topology in cascade.
For a start, find the gain as the frequency goes to zero (open the capacitors, short the inductors) and the gain as the frequency goes to infinity (short the capacitors, open the inductors).
Given just the four categories of filters you've listed, you have the following possibilities:
If the gain goes to zero at both extremes, you have a band-pass filter.
If the gain is the same at both extremes, you have a band-reject filter
If the gain only goes to zero at one extreme, you have either a low-pass or a high-pass filter.
Of course, there are other possible filters to consider such as, e.g., shelving filters and all-pass filters etc.
Now, looking at the circuit you've posted...
with the capacitors open, the gain is 1.
with the capacitors shorted, the gain is 0.
Thus, this circuit is a low-pass filter.