Eisenstein series are important examples for modular forms, for instance they are the simplest vector-valued modular forms. Hence it is a quite interesting problem to determine when they are holomorphic. In the paper under review, the author considers this problem for the half-integral weight vector-valued case, namely \(3/2\). Let \(\underline{L}\) be an even lattice. Then Brandon Williams shows that Eisenstein series \(E_{3/2}\) are often non-holomorphic by so-called Hecke’s trick, so the questions arises: when are they holomorphic, under which condition(s)? Then in the paper under review, the author answers this question as the following: if there exists an odd prime \(p\) such that \(\underline{L}\) is local \(p\)-maximal and the determinant of \(\underline{L}\) is divisible by \(p^2\), then the Eisenstein series of weight \(3/2\) attached to the discriminant form of \(\underline{L}\) is holomorphic. The proof is based on some calculations on complex analysis.