list manipulation - Map works but Thread doesn't

This question may be trivial, but I can't get past it for the life of me.

I have $n$ matrices of dimension $p_i \times N_i$, with $i$ indexing the $n$-set. I also have $n$ vectors of the appropriate length.

I'm looking to create a list of the inner products. This works (obviously):

MapThread[Dot[#1,#2]&,{nmats,nvecs}]

The problem comes in when I pass in lists of nmats. That is, I have $C$ copies of nmats stored in cnmats and want to collect the above for each. For some reason Mapping works,

MapThread[Dot[#1,#2]&,{#,nvecs}]&/@cnmats

but Threading doesnt

Thread[MapThread[Dot[#1,#2]&,{#,nvecs}]&[cnmats]]

Replacing MapThread with Table moves the error to Dot: Nonrectangular tensor encountered.

The error returned is:

Incompatible dimensions of objects at positions {2, 1} and {2, 2} of (MapThread expression);
dimensions are n and C

$C$ and $N_i$ are $O(10^5)$, $p$ is $O(1)$, so I favor Thread for the speed advantage.

Why can't I thread here? How can I implement this differently to benefit from threading?