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We investigate the spatial extent of the [CII] line emission in a sample of 34 galaxies at $z=4-6$ from the ALMA-CRISTAL Survey. By modeling the [CII] line emission in the visibility data directly, we derive the effective radius of [CII] line emission assuming exponential distribution. These measurements comprise not only isolated galaxies but also interacting systems, identified thanks to the high spatial resolution of the data. The [CII] line radius ranges from 0.5 to 3.5 kpc with an average value of 1.9 kpc. We compare the [CII] sizes with the sizes of UV and FIR continua, which were measured from the HST F160W and ALMA Band-7 continuum images, respectively. We confirm that the [CII] line emission is more spatially extended than the continuum emission, with average size ratios of $R_{e,[CII]}/R_{e,UV}=2.90$ and $R_{e,[CII]}/R_{e,FIR}=1.54$, although about half of the FIR-detected sample show comparable spatial extent between [CII] line and FIR continuum emission ($R_{e,[CII]}\approx R_{e, FIR}$). The residual visibility data of the best-fit model do not show evidence of flux excesses either individually or in stacking analysis. This indicates that the [CII] line emission in star-forming galaxies can be characterized by an extended exponential disk profile. Overall, our results suggest that the spatial extent of [CII] line emission can primarily be explained by photodissociation regions associated with star formation activity, while the contribution from diffuse neutral medium (atomic gas) and the effects of mergers may further expand the [CII] line distributions, causing their variations among our sample. We report the correlations between the [CII] line, dust, and Lya line properties, which may be in line with our scenario. Future 3D-analysis of Lya and Ha lines will shed light on the association of the extended [CII] line emission with atomic gas and outflows., Comment: Submitted to A&A, 21 pages, 14 figures, 4 tables