Summary: We consider a family \(\{L_t,\ t\in [0,T]\}\) of closed operators generated by a family of regular (non-symmetric) Dirichlet forms \(\{(B^{(t)}, V), t \in [0,T]\}\) on \(L^2(E;m)\). We show that a bounded (signed) measure \(\mu\) on \((0,T) \times E\) is smooth, i.e. charges no set of zero parabolic capacity associated with \(\frac{\partial}{\partial t} + L_t\), if and only if \(\mu\) is of the form \(\mu = f \cdot m_1 + g_1 + \partial_t g_2\) with \(f \in L^1((0,T)\times E; \text{d}t \otimes m)\), \(g_1 \in L^2(0,T; V')\), \(g_2 \in L^2(0,T; V)\). We apply this decomposition to the study of the structure of additive functionals in the Revuz correspondence with smooth measures. As a by-product, we also give some existence and uniqueness results for solutions of semilinear equations involving the operator \(\frac{\partial}{\partial t} + L_t\) and a functional from the dual \(\mathcal{W}'\) of the space \(\mathcal{W} = \{u \in L^2(0,T; V) : \partial_t u \in L^2(0,T; V')\}\) on the right-hand side of the equation.