Constraints on the lifetime of the heavy sterile neutrino, that was proposed as a possible interpretation of the KARMEN anomaly, are derived from primordial nucleosynthesis and SN 1987A. Together with the recent experimental bounds on the nu(s), lifetime, SN 1987A completely excludes this interpretation. Nucleosynthesis. arguments permit a narrow window for the lifetime in the interval 0.1-0.2 s. If nu(s) possesses an anomalous interaction with nucleons, the SN bounds may not apply, while the nucleosynthesis ones would remain valid. (C) 2000 Elsevier Science B.V. All rights reserved.