During the untap step, permanents you control normally untap automatically under CR 502.3. However, some card effects replace or modify this by saying you may untap a permanent. The word 'may' always signals an optional action in Magic (CR 101.2), so you are never forced to untap when the effect uses that word.
This distinction matters most when a permanent has a beneficial tapped state, or when untapping it would trigger a negative consequence. Because 'may untap' is a permission, not a requirement, you simply decline to use it and the permanent stays tapped.
Note that this is different from the normal untap step, where untapping is automatic and you generally cannot choose to keep a permanent tapped unless a specific effect (like a static ability saying 'this doesn't untap during your untap step') prevents it (CR 502.3). A 'may untap' ability replaces or supplements that normal process with a genuine choice.
Example: You control a creature enchanted with an Aura that reads 'At the beginning of your untap step, you may untap enchanted creature.' Your creature is tapped and you want it to stay that way to avoid a 'whenever this creature untaps' trigger on your opponent's permanent. You simply say 'No, I choose not to untap it,' and it remains tapped for the turn.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.