  We present and analyze correlation functions of a main-chain polymer nematic
in a continuum worm-like chain description for two types of constraints
formalized by the tensorial and vectorial conservation laws, both originating
in the microscopic chain integrity, i.e., the conectivity of the polymer
chains. In particular, our aim is to identify the features of the correlation
functions that are most susceptible to the differences between the two
constraints. Besides the density and director autocorrelations in both the
tensorial and vectorial cases, we calculate also the density -- director
correlation functions, the latter being a direct signature of the presence of a
specific constraint. Its amplitude is connected to the strength of the
constraint and is zero if none of the constraints is present, i.e., for a
standard non-polymeric nematic. Generally, the correlation functions with the
constraints differ substantially from the correlation functions in the
non-polymeric case, if the constraints are strong which in practice requires
long chains. Moreover, for the tensorial conservation law to be well
distinguishable from the vectorial one, the chain persistence length should be
much smaller than the total length of the chain, so that hairpins (chain
backfolding) are numerous and the polar order is small.
