We report the temperature dependencies of the upper critical fields $H_{ctext{2}}^{text{c}}(T)$ parallel to the c-axis and $H_{ctext{2}}^{text{ab}}(T)$ parallel to the ab-plane of single crystalline CaKFe$_4$As$_4$ inferred from the measurements of the temperature-dependent resistance in static magnetic fields up to 14 T and magnetoresistance in pulsed fields up to 63 T. We show that the observed decrease of the anisotropy parameter $gamma(T)=H_{ctext{2}}^{text{ab}}/H_{ctext{2}}^{text{c}}$ from $simeq 2.5$ at $T_c$ to $simeq 1.5$ at 25 K can be explained by interplay of paramagnetic pairbreaking and orbital effects in a multiband theory of $H_{c2}$. The slopes of $dH_{ctext{2}}^{text{c}}/dTsimeq-4.4$ T/K and $dH_{ctext{2}}^{text{ab}}/dT simeq-10.9$ T/K at $T_c$ yield an electron mass anisotropy of $m_{ab}/m_csimeq 1/6$ and short coherence lengths $xi_csimeq 5.8,text{AA}$ and $xi_{ab}simeq 14.3,text{AA}$. The behavior of $H_{ctext{2}}(T)$ turns out to be similar to that of the optimal doped (Ba,K)Fe$_2$As$_2$, with $H_{ctext{2}}^{text{ab}}(0)$ extrapolating to $simeq 92$ T, well above the BCS paramagnetic limit.
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