"Tom", Michael Corleone said, "I'm driving down to the city with Kay tommorow. There's something important I want to tell the old man before Christmas. Will he be home tommorow night?"
"Sure," Hagen said "He's not going out of town until after Christmas. Anything I can do for you?"
Michael was as closemouthed as his father. "No," he said...
1 Answer
Closemouthed can generally mean that the person was not talking at all. Or it can mean that a person is talking, most people need to open their mouth to talk, but just not speaking of the details or not giving out very much information.
In this case, it seems that Michael and the father were up to something, and didn't want Hagen to know what they were up to. Which is why he just answered No when Hagen asked if there was anything he could do for him.