At present, study of the novel Compton telescope with high sensitivity has great scientific significance. The calorimeter, as one of the important components of the Compton telescope, is required to have excellent energy resolution and position resolution. For this purpose, a CsI(Tl) $\gamma $
-ray detector of dual-ended readout based on silicon photomultipliers (SiPM) was designed as the basic detection unit of the calorimeter for the Compton telescope. Different wrapping materials (Teflon, Tyvek and ESR) and different crystal sizes (5 mm×5 mm×60 mm, 5 mm×5 mm×80 mm and 5 mm×5 mm×100 mm) were used to construct the detectors, and the detectors were tested with a 137
Cs source. The influence of the wrapping materials was not significant to the energy resolution but quite pronounced to the light attenuation length and position resolution. Besides, the light attenuation length and position resolution showed strong correlation, i.e.
the shorter light attenuation length corresponding to the better the position resolution; In addition, for the three detectors using different sizes of the crystals, they did not show significant differences in performance. Eventually, the CsI(Tl) crystal detector with the size of 5 mm×5 mm×80 mm and the wrapped with ESR was determined to construct the detector satisfied with the requirements of the calorimeter for the novel Compton telescope. The energy resolution can reach 5.2% and the position resolution is about 5.2 mm.