  We study the data complexity of consistent query answering (CQA) on databases
that may violate the primary key constraints. A repair is a maximal consistent
subset of the database. For a Boolean query $q$, the problem
$\mathsf{CERTAINTY}(q)$ takes a database as input, and asks whether or not each
repair satisfies $q$. It is known that for any self-join-free Boolean
conjunctive query $q$, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$,
$\mathbf{LSPACE}$-complete, or $\mathbf{coNP}$-complete. In particular,
$\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$ for any self-join-free Boolean path
query $q$. In this paper, we show that if self-joins are allowed, the
complexity of $\mathsf{CERTAINTY}(q)$ for Boolean path queries $q$ exhibits a
tetrachotomy between $\mathbf{FO}$, $\mathbf{NL}$-complete,
$\mathbf{PTIME}$-complete, and $\mathbf{coNP}$-complete. Moreover, it is
decidable, in polynomial time in the size of the query~$q$, which of the four
cases applies.
