The first kind of muon–catalyzed fusion to be observed experimentally, by L.W. Alvarez et al., was protium (H or H) and deuterium (D or H) muon-catalyzed fusion.  The fusion rate for p–d (or pd) muon-catalyzed fusion has been estimated to be about a million times slower than the fusion rate for d–t muon-catalyzed fusion.
Of more practical interest, deuterium–deuterium muon-catalyzed fusion has been frequently observed and extensively studied experimentally, in large part because deuterium already exists in relative abundance and, like protium, deuterium is not at all radioactive. (Tritium rarely occurs naturally, and is radioactive with a half-life of about 12.5 years.)
The fusion rate for d–d muon-catalyzed fusion has been estimated to be only about 1% of the fusion rate for d–t muon-catalyzed fusion, but this still gives about one d–d nuclear fusion every 10 to 100 picoseconds or so.  However, the energy released with every d–d muon-catalyzed fusion reaction is only about 20% or so of the energy released with every d–t muon-catalyzed fusion reaction.  Moreover, the catalyzing muon has a probability of sticking to at least one of the d–d muon-catalyzed fusion reaction products that Jackson in this 1957 paper estimated to be at least 10 times greater than the corresponding probability of the catalyzing muon sticking to at least one of the d–t muon-catalyzed fusion reaction products, thereby preventing the muon from catalyzing any more nuclear fusions. Effectively, this means that each muon catalyzing d–d muon-catalyzed fusion reactions in pure deuterium is only able to catalyze about one-tenth of the number of d–t muon-catalyzed fusion reactions that each muon is able to catalyze in a mixture of equal amounts of deuterium and tritium, and each d–d fusion only yields about one-fifth of the yield of each d–t fusion, thereby making the prospects for useful energy release from d–d muon-catalyzed fusion at least 50 times worse than the already dim prospects for useful energy release from d–t muon-catalyzed fusion.
Potential "aneutronic" (or substantially aneutronic) nuclear fusion possibilities, which result in essentially no neutrons among the nuclear fusion products, are almost certainly not very amenable to muon-catalyzed fusion.  One such essentially aneutronic nuclear fusion reaction involves a deuteron from deuterium fusing with a helion (He) from helium-3, which yields an energetic alpha particle and a much more energetic proton, both positively charged (with a few neutrons coming from inevitable d–d nuclear fusion side reactions).  However, one muon with only one negative electric charge is incapable of shielding both positive charges of a helion from the one positive charge of a deuteron.  The chances of the requisite two muons being present simultaneously are exceptionally remote.