What properties specifically are you referring to? It sounds like you're referring to the same specified properties mentioned above, which aren't accessible via the API. Whether or not properties are required on object creation or are included in the object's 'about' section isn't something that you can access via the API. Your best bet would likely be to allow your users to set those options separately in your app.
Users with administrative access can set up required fields for contacts, companies, and deals in HubSpot.
It's not currently possible to access these settings via the API; contacts created via the API don't need to obey these requirements. I can see the use case for a 'Required Properties API,' however: If you have the inclination, I would encourage you to check out the Ideas Forum on the HubSpot Community. There, you can create a post including your use case that product and other customers can see.