The pattern of anisotropies in the cosmic microwave background depends
upon the masses and lifetimes of the three neutrino species. A neutri
no species of mass greater than 10 eV with lifetime between 10(13) and
10(17) sec leaves a very distinct signature (due to the integrated Sa
chs-Wolfe effect): the anisotropies at large angles are predicted to b
e comparable to those on degree scales. Present data exclude such a po
ssibility and hence this region of parameter space. For m(v) similar o
r equal to 30 eV, tau similar or equal to 10(13) sec, we find an inter
esting possibility: the integrated Sachs-Wolfe peak produced by the de
caying neutrino in low-Omega models mimics the acoustic peak expected
in an Omega = 1 model. [S0031-9007(98)07347-5].