Usually to do this you will need to have another citizenship since being stateless is not something you should become unless there are dire circumstances. If that's the case, then what you usually need to do is go to another country and declare yourself as a refugee. Rules vary country to country.
Assuming that you already have another citizenship the process to renounce Peruvian citizenship is pretty straightforward. You have two choices: you can either do it at a Peruvian embassy/consulate abroad or in Lima at the Superintendencia Nacional de Migraciones aka migraciones. The information below was taken from the Chicago consulate's website:
- Bring your DNI (or Libreta Militar) and passport.
- Bring the solicitud to renounce Peruvian citizenship.
- Pay the fee.
- You'll be registered as wishing to renounce citizenship.
The information above it only for those over the age of 18. You're not allowed to renounce citizenship on behalf of a minor. If you aren't sure if you want to renounce Peruvian citizenship or if you're hoping your minor children will do it in the future, here are somethings you can do.
- First,change your DNI to show an address abroad so you won't be fined for not voting.
- Secondly, cut ties with Peru: close bank accounts, sell property, don't visit, etc.
- Third, even though it might be tempting to destroy documents such as birth, marriage, or death certificates, or your DNI or passport: don't do it. Just keep them since destroying them could cause you legal problems.
- Lastly, don't renew your DNI or passport. Simply let them expire. For all intents and purposes Peru won't be able to keep tabs on you and you can just disappear.