A broader meaning can be found here: wsjp.pl/haslo/podglad/18023/jakby-kij-polknal
"w sposób sztywny, pozbawiony spontaniczności, nienaturalny" (in a stiff, unspontaneous manner, unnaturally) which is closer to the context I first came across it in a detective novel (complaining about a colleague's over-bureaucratic manner of speaking).