  Scalar non-standard interactions (NSI) presents an exciting pathway for
probing potential new physics that extends beyond the Standard Model (BSM). The
scalar coupling of neutrinos with matter can appear as a sub-dominant effect
that can impact the neutrino oscillation probabilities. The uniqueness of these
interactions is that it can directly affect the neutrino mass matrix. This
makes oscillations sensitive to the absolute neutrino mass. The effects of
scalar NSI scales linearly with matter density which motivates its exploration
in long-baseline sector. The presence of scalar NSI can influence the key
measurements in the field of neutrino physics, including the precise
determination of the leptonic CP phase ($\delta_{CP}$), neutrino mass ordering
and the octant of $\theta_{23}$. The precise determination of $\delta_{CP}$ is
one of the major goals of DUNE, which is an upcoming long-baseline experiment.
A better understanding of the impact of scalar NSI on CP measurement
sensitivities is crucial for accurate interpretation of $\delta_{CP}$ phase. In
this work, we have explored the impact of the complex off-diagonal scalar NSI
elements $\eta_{\alpha\beta}$ and their associated phases $\phi_{\alpha\beta}$
on the CP-measurement sensitivities at DUNE. We have explored the impact of the
neutrino mass scale on these sensitivities. We look for constraining these
off-diagonal elements for different neutrino mass scales. We also explore their
correlation with $\delta_{CP}$, investigating potential degeneracies that can
arise due to additional phases. We also perform a correlation study among
different scalar NSI elements. We show that the inclusion of the complex scalar
NSI elements can significantly modify the CP phase measurements.
