I can tell you this, if an officer wishes to arrest you "without" a warrant, the offense MUST be committed in his presence:
§ 2-202. Warrantless arrests - In general.
(a) Crimes committed in presence of police officer.- A police officer may arrest without a warrant a person who commits or attempts to commit a felony or misdemeanor in the presence or within the view of the police officer.
I have not sifted through the shoplifing laws, but some states permit a warrantless arrest, as an exception, if the theft ocurred within a reasonable time after it, even though it was not "in presence", the same with domestic violence, etc., generally.
IF a complaint is made for theft, in order to be arrested they would have to issue a warrant. Most probably a citation/summons will be sent to you if charges are brought.
Warrants take manpower to execute, a summons can be mailed.

