I can't give you a full answer at the moment but I can at least provide you with this exert from Seneca, a Roman Stoic Philosopher who was tutor to the Emperor Nero for a time. He described a proposal in the senate for slaves to wear some sort of identification to distinguish them from the free. Seneca argued against such an institution and so did the majority of the senate, out of fear that if slaves could identify each other they would become aware of their great numbers. (Seneca, De Clementia) Keeping in mind that Rome had 3rd large scale servile wars (the 3rd involving Spartacus, which ended with thousands of slaves being cruxcified by Crassus).

If you're interested in slaves in antiquity Keith R. Bradley and M.I Finley are the experts on the topic. Also have a read of Seneca's Letter on Morales 47, you'll find an interesting perspective from the Stoic Philosopher on the treatment of slaves.

TLDR: It was almost impossible to identify slaves in urban areas as many acted as agents with authority on behalf of their masters, were dressed well (or similar to the free poor), they worked in trades and crafts, as prostitutes, teachers, accountants, scribes. However in Rome, some who ran away were branded or wore collars.

EDIT: sorry about the formating and poor referencing. On my phone.

In support of Valinorification, here's a passage from the Old Oligarch (aka Pseudo-Xenophon):

Now among the slaves and metics2 at Athens there is the greatest uncontrolled wantonness; you can't hit them there, and a slave will not stand aside for you. I shall point out why this is their native practice: if it were customary for a slave (or metic or freedman) to be struck by one who is free, you would often hit an Athenian citizen by mistake on the assumption that he was a slave. For the people there are no better dressed than the slaves and metics, nor are they any more handsome.

Our author doesn't give any indication that slaves or metics (Athens' form of green card) were marked in some way. Instead he thinks you should be able to tell them apart based on wealth.

Not an answer but a follow-up question: during the era of the French and American revolutions, one of the ubiquitous symbols of liberty was the red liberty cap, or "Phrygian bonnet". According to several sources I have read, this symbolism has to do with the fact that the Phrygian cap was worn by emancipated slaves in ancient Rome and thus was associated with a primitive form of liberty. Is there any truth to this? Did former slaves actually wear red caps?