This seems to be a rather complicated issue. The earliest source I've been able to find proposed the existence of a muon counterpart to the electron neutrino is Sakata & Inoue's On the Correlations between Mesons and Yukawa Particles, published in English in 1946 but formulated several years prior. They postulated the existence of a charged meson $m^{\pm}$ and a neutral meson $n$ which could interact with the then-called "Yukawa meson" $Y^{\pm}$ (the charged pion) by
$$m^{\pm}\leftrightarrow n+Y^{\pm},\quad n\leftrightarrow m^{\pm}+Y^{\mp}$$
In particular, they described $n$ as a
neutral meson which is assumed in the following discussions to have a negligible mass, and consequently may be regarded as equivalent with the neutrino
Decades later (I can't determine the precise data), Masami Nakagama wrote in Neutrinos and Sakata: A Personal View that it was later assumed by many "from the convenience and economy principles" that the beta decay neutrinos (electron neutrinos) and the "neutral mesons" of Sakata and Inoue were the same, something Sakata apparently resisted. In conjunction with Sakata's objections, Ogama & Kamefuchi's On the µ-Meson Decay explored some problematic consequences of assuming that the two particles were identical, meaning that the debate was going on as of 1950. The upshot? It seems that the community may have shifted from the idea that there was a sibling to the [electron] neutrino to the idea that this particle was the same as the neutrino; then shifted back in the aftermath of the 1962 experiments at Brookhaven (interestingly enough, the Danby et al. paper reporting the experiments mentions none of the abovementioned theories).
An additional reason I say that this is complicated is that proponents of the distinct-particle theory might not have still classified both particles under the umbrella of "neutrino" - in other words, it's not clear to me that Sakata & Inoue intended for their "neutral meson" to be thought of as a true sibling to the neutrino, or just an analogous counterpart in a pair of sort-of-analogous interactions. But that may not be an objection that others think is substantial.