First of all, there is no state in a socialist utopia. Unless you mean socialist in the sense of having a dictatorship of the proletariat, but would not call that a utopia.

Usually Marxists find speculating about the specifics of the far future communist society pretty pointless. No one can really know how it will look. I would assume there would be some system to measure the society's needs and arrange what work is necessary to fulfill them to be done.

"In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor, and therewith also the antithesis between mental and physical labor, has vanished; after labor has become not only a means of life but life's prime want; after the productive forces have also increased with the all-around development of the individual, and all the springs of co-operative wealth flow more abundantly – only then can the narrow horizon of bourgeois right be crossed in its entirety and society inscribe on its banners: From each according to his ability, to each according to his needs!" -Marx, Critique of the Gotha Programme