Light trans-iron elements such as Sr serve as the key to understanding the astrophysical sites of heavy elements. Spectroscopic studies of metal-poor stars have revealed large star-to-star scatters in the ratios of [Sr/Ba], which indicates that there are multiple sites for the production of Sr. Here we present the enrichment history of Sr by a series of the $N$-body/smoothed particle hydrodynamics simulations of a dwarf galaxy with a stellar mass of 3 $times$ 10$^{6}$ $M_{odot}$. We show that binary neutron star mergers (NSMs) and asymptotic giant branch (AGB) stars contribute to the enrichment of Sr in the metallicity ranges [Fe/H] $gtrsim$ $-$3 and [Fe/H] $gtrsim$ $-$1, respectively. It appears insufficient, however, to explain the overall observational trends of Sr by considering only these sites. We find that the models including electron-capture supernovae (ECSNe) and rotating massive stars (RMSs), in addition to NSMs and AGBs, reasonably reproduce the enrichment histories of Sr in dwarf galaxies. The contributions of both ECSNe and NSMs make scatters of $approx$ 0.2 dex in [Sr/Fe], [Sr/Ba], and [Sr/Zn] as can be seen for observed stars in the metallicity range [Fe/H] $<$ $-2$. We also find that the mass range of ECSN progenitors should be substantially smaller than $1, M_odot$ (e.g., 0.1-$0.2, M_odot$) to avoid over-prediction of [Sr/Ba] and [Sr/Zn] ratios. Our results demonstrate that NSMs, AGBs, ECSNe, and RMSs all play roles in the enrichment histories of Local Group dwarf galaxies, although more observational data are required to disentangle the relative contributions of these sources.
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