The blowings of the Shofar during the Musaf prayer on Rosh Hashanah, should be done by someone other than the Hazzan, because we fear that he will get confused. However, if he is certain that he will be able to return to the Musaf prayer without getting confused, he may blow the Shofar during Musaf also.
The one who blows the first 30 calls of the Shofar, which are called "DeMeyosheb" (while one is sitting), should also be the one who blows during Musaf, because we have a concept that the one who begins a commandment is told to complete it. However, if the Hazzan is the one who blew the first 30 calls, he is not told to complete the rest, unless he will not become confused, as we have just mentioned.
(See Kaf HaHayim See Shulhan 'Arukh 685:4 with Rama)
