  We present results of several measurements of CsI[Na] scintillation response
to 3-60 keV energy nuclear recoils performed by the COHERENT collaboration
using tagged neutron elastic scattering experiments and an endpoint technique.
Earlier results, used to estimate the coherent elastic neutrino-nucleus
scattering (CEvNS) event rate for the first observation of this process
achieved by COHERENT at the Spallation Neutron Source (SNS), have been
reassessed. We discuss corrections for the identified systematic effects and
update the respective uncertainty values. The impact of updated results on
future precision tests of CEvNS is estimated. We scrutinize potential
systematic effects that could affect each measurement. In particular we confirm
the response of the H11934-200 Hamamatsu photomultiplier tube (PMT) used for
the measurements presented in this study to be linear in the relevant signal
scale region.
