  We constrain the cosmic ray (CR) population in the circumgalactic medium
(CGM) of Milky Way by comparing the observations of absorption lines of OVIII
ion with predictions from analytical models of CGM : precipitation (PP) and
isothermal (IT) model. For a CGM in hydrostatic equilibrium, the introduction
of CR suppresses thermal pressure, and affects the OVIII ion abundance. We
explore the allowances given to the ratio of CR pressure to thermal pressure
($\rm{P}_{\rm{CR}}/\rm{P}_{\rm{th}}=\eta$), with varying boundary conditions,
CGM mass content, photoionization by extragalactic ultraviolet background and
temperature fluctuations. We find that the allowed maximum values of $\eta$ are
: $\eta\lesssim10$ in the PP model and $\eta\lesssim6$ in the IT model. We also
explore the spatial variation of $\eta$ : rising ($\eta=Ax$) or declining
($\eta=A/x$) with radius, where A is the normalization of the profiles. In
particular, the models with declining ratio of CR to thermal pressure fare
better than those with rising ratio with suitable temperature fluctuation
(larger $\sigma_{\rm ln T}$ for PP and lower for IT). The declining profiles
allow $A\lesssim8$ and $A\lesssim10$ in the case of IT and PP models,
respectively, thereby accommodating a large value of $\eta \,(\simeq 200)$ in
the central region, but not in the outer regions. These limits, combined with
the limits derived from $\gamma$-ray and radio background, can be useful for
building models of Milky Way CGM including CR population. However, the larger
amount of CR can be packed in cold phase which may be one way to circumvent
these constraints.
