basics of Chern-Simons electrodynamics defined on a four dimensional spacetime in which the $\theta $-value is piecewise constant in different regions of space separated by a common boundary $\Sigma $. In section \[Green\] we restrict ourselves to the static case and we construct the GF matrix for the planar geometry corresponding to a $\theta $-boundary located at $z=a$. Section \[applications\] is devoted to different applications, *e.g.*, the problems of a point-like charge and a current-carrying wire near a planar $\theta $-boundary. The interaction energy (and forces) between a charge-current distribution and a $\theta $-interface is briefly discussed. Contact between the results obtained with our method and others in the existing literature is made. A concluding summary of our results comprises the last section \[summary\]. Throughout the paper, Lorentz-Heaviside units are assumed ($\hbar =c=1$), the metric signature will be taken as $\left( +,-,-,-\right) $ and the convention $\epsilon ^{0123}=+1$ is adopted.

$\protect\theta$-Electrodynamics in a bounded region {#model}
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Our model is based on Maxwell electrodynamics coupled to a gauge invariant $\theta$-term as described by the following action $$\mathcal{S}=\int_{\mathcal{M}}d^{4}x\left[ -\frac{1}{16\pi }F_{\mu \nu
}F^{\mu \nu }-\frac{1}{4}{\theta }\frac{\alpha }{4\pi^2 }F_{\mu
\nu }\tilde{F}^{\mu \nu }-j^{\mu }A_{\mu }\right] ,  \label{action}$$where $\alpha =e^{2}/\hbar c$ is the fine 