A strontium iodide crystal doped by europium (SrI 2 (Eu)) was produced by using the Stockbarger growth technique. The crystal was subjected to a characterization that includes relative photoelectron output and energy resolution for γ quanta. The intrinsic radioactivity of the SrI 2 (Eu) crystal scintillator was tested both by using it as scintillator at sea level and by ultra-low background HPGe γ spectrometry deep underground. The response of the SrI 2 (Eu) detector to α particles (α/β ratio and pulse shape) was estimated by analysing the 226 Ra internal trace contamination of the crystal. We have measured: α/β=0.55 at Eα=7.7MeV, and no difference in the time decay of the scintillation pulses induced by α particles and γ quanta. The application of the obtained results in the search for the double electron capture and electron capture with positron emission in 84 Sr has been investigated at a level of sensitivity: T1/2∼1015–1016yr. The results of these studies demonstrate the potentiality of this material for a variety of scintillation applications, including low-level counting experiments.