अल्छिको राजा,

If Nepal were to accept dual citizenship, you wouldn't have to renounce your American citizenship to get a Nepali citizenship (unless Nepal is to put some restriction). That means US have dual citizenship provision. However, if you are a Nepali citizen but want to be a naturalized US citizen, you'll need to renounce your current citizenship in order to get one. The renouncement is not enforced with some documentation but through verbal commitment when you take the oath.

Some countries, like Singapore, requires official renunciation of old citizenship in order to get theirs.