We present a brief review of experimental status in searching for hypothetical sterile neutrino in nuclear decay in laboratory testing. The main idea is based on search for an additional small component in the β-spectrum or a shift in the internal electron conversion energy. For example, in a three-body β-decay it looks like a kink in the continuous spectrum shifted by the value of sterile neutrino mass from the spectrum endpoint. After a short general motivation for such a search we discuss the way how to find sterile neutrino in the nuclear β-decay and present the current status of upper limits on sterile neutrino mixing with electron antineutrino. The advantages and problems arising in the precise measurements of β-spectrum are demonstrated on the basis of the “Troitsk nu-mass” experiment by presenting the all measurement and analysis procedures in details. At the end we discuss the nearest future of such experiments.