I guess you already know the general rules about when you should use formal tone, and want to know how to say if you believe you can speak to them in casual tone (ex. your friends) but you don't sure so you want to ask to make sure, like "Can I call you by name", right? If so, then you can use it: "タメ口で話してもいいですか？" or "タメで話してもいいですか？". In hiragana, "ためぐちではなしてもいいですか？" or "ためではなしてもいいですか？" Younger people prefer to use the latter, as far as I heard. FYI "タメ口" or "タメ" means "casual talking". If not, let us know the detailed situation. thx:)

Are you familiar with the senpai-kohai concept in Japan? If you have never heard of it, I can explain but if you already know, it's quite simple. If you're a senpai (usually older) to a person whom you're speaking with, you're automatically allowed to use casual speech.

I think it's better if you stick to the fundamental rules in speaking with the Japanese: 1. Always use formal speech when speaking to a Japanese with older age/higher rank (your boss/colleague) than yours. Ex. always say Ohayou Gozaimasu (not just ohayou) to them and don't forget to add "San" to their surnames, when addressing them, such as Hirohito San, Yamamoto San.. Also, a "bow" is expected, even though you don't say a word to them. 2. Use informal speech if you are speaking to Japanese who are younger than you or to your Japanese friends whom you've already known for a while. Ex. you may simply say Ohayou and drop the gozaimasu.. You don't need to ask them.. it should already be in your system... just remember that the japanese are modest and humble people, so you should approach them the same way.

I don't know any Japanese so it's difficult to advise you. In European languages like German, French and Italian which have a formal 'you' this may be dropped after a relationship has been established and the more senior of the two people requests that they change to the informal 'you'. In English we don't have a formal 'you'. We use more formal language in a business/ formal environment / with people we don't know (strangers in the street) or when making requests or offers to people who are not friends or family. Informal English is usually used with people we know well or in an informal environment. When there is a change in the relationship from formal to informal the change in language happens naturally.

You don't ask, it just happens. How do you know if you are friends with someone or if you only have a business relation? Do you ask? No. It's usually obvious.