EpsContractFreeQ[exp] returns True if the expression contains epsilon tensors that can be contracted with each other. The function is optimized for large expressions, i.e. it is not so good as a criterion in e.g. Select.
Overview, Contract, EpsContract.
FCI[LC[p1, p2, p3, p4]]
EpsContractFreeQ[%]\bar{\epsilon }^{\text{p1}\;\text{p2}\;\text{p3}\;\text{p4}}
\text{True}
FCI[LC[p1, p2, p3, mu] LC[q1, q2, q3, q4]]
EpsContractFreeQ[%]
\bar{\epsilon }^{\text{p1}\;\text{p2}\;\text{p3}\;\text{mu}} \bar{\epsilon }^{\text{q1}\;\text{q2}\;\text{q3}\;\text{q4}}
\text{False}