No default system prompt in the API. There are some topics I much prefer chatting with the API due to system prompt of the web front-end being so restrictive (eg. song lyrics). In general I recommend people to try the API with no system prompt to more accurately see what the default tone of a model is.

There is still some sort of system prompt even through the API. It will still refuse to give you medical/legal/financial advice and so on.

That behavior is baked in the model via RLHF, it doesn't require a specific prompt.