We construct the $g$-loop $N$-string vertex using the Feynman-like rules in the operator formalism with bosonized $\mathrm{bc}$ ghosts. The measure factor is analyzed in detail, which consists of the ghost $g$ vacuum and the contour integration associated with the $b$-ghost insertion. The general form of the $g$ vacuum is derived using the handle operators. The handle operator is formulated by the geometrical quantities: period matrix, first Abelian integral, prime form, ½ differential, and Riemann constant. Explicit results are given up to two-loop level. The contour integrations associated with the ghost insertions can be performed explicitly in the one-loop case, in which we reproduce the well-known formula of the one-loop $N$-tachyon amplitude.

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