It is marked on a passport with a red stamp showing a cross next to the text ENTRY DENIED. The stamp also features the current in-game date (or November 23rd, 1982 in the latest beta) and a shield icon also featured in the Ministry of Admission seals.
One should be denied entry to Arstotzka if they fail to meet the requirements stated in the immigration protocol, e.g. invalid papers, possession of contraband, etc. Denying entry to an entrant with valid documents will lead to a citation
Care must be taken when denying entry. Once the inspector has stamped a passport with the entry denial stamp, no matter how many times the inspector later stamps the passport with the entry approval stamp, the entrant will be denied.