Can I use OAuth2 to get user's zoho email?

Our company has a site with authorization ability. Everyone in company has his own zoho account, so I decided to make authorization on site through zoho.

Now I found this solution (very bad, but for example) using ZohoCRM API:

On login page of my site user clicks link https://accounts.zoho.com/oauth/v2/auth?scope=ZohoCRM.users.READ&response_type=code&redirect_uri=http://mysite.com/oauth2&client_id=<my_client_id>, give access for reading ZohoCRM users information and returns to http://mysite.com/oauth2 with code;
I use given code to get access-token from https://accounts.zoho.com/oauth/v2/token as it described in ZohoCRM AP;
Then I call https://www.zohoapis.com/crm/v2/users?type=CurrentUser to get array of users, where first user is he who is trying to log into my site, so I get his email, verify it is like <username>@mysite.com and authorize user on my site with his username.

This works great, but not for those who doesn't work with ZohoCRM, the just get error on the third step, becouse the havn't any access to ZohoCRM.