Carrying passport and travelling in Cyprus

I believe so but in reality not likely ... Or even practical

Even EU and non EU residents by law should also carry their permits .  But they dont.. I've been here.10 years and not once have I been asked for my passport or residency permit ... Except at immigration, the north border and airport....

I NEVER leave my passport anywhere when travelling.

I suggest keeping it in a hidden wallet

You may or may not get asked for it, but it won't go missing from a hotel room

@Harmanjeet Singh As per the message of Toon what he says makes total sense. only one suggestion. Have a copy of photo page and entry visa. COPY ONLY.

Carry copies on your mobile phone....  Most people carry their phone everywhere

    Even EU and non EU residents by law should also carry their permits .  But they dont.. I've been here.10 years and not once have I been asked for my passport or residency permit ... Except at immigration, the north border and airport....        -@Toon

This is what I was told by the British Embassy in Austria, even when the UK was in the EU and the rule still applies. You don't have to have the passport on the person but you must be able to get to it within an hour if asked by the police to see it.

But in all the places I have lived I have never been stopped or asked to produce it.

    Carry copies on your mobile phone....  Most people carry their phone everywhere
   

    -@Toon

Exactly, I have a copy of all my papers on my phone.

@SimCityAT

Me too  .... all my important documents