Rest API parameter are case-sensitive, Like User_Id and user_id are not interchangeable. But are services URLs also case-sensitive?
As per salesforce documentation:
The URL mapping is case-sensitive. A URL mapping for my_url will only match a REST resource containing my_url and not My_Url.
Also if you are packaging your REST Service in a managed package your package namespace prefix is also case-sensitive.
The URL for a namespaced classes contains the namespace. For example, if your class is in namespace abc and the class is mapped to your_url, then the API URL is modified as follows: https://instance.salesforce.com/services/apexrest/abc/your_url/. In the case of a URL collision, the namespaced class is always used.
In above example if your namespace is abc you can't use ABC, Abc or any other variation of upper/lower case namespace.
I agree to Amit and its true about custom API.
But for standard API the URI are case insensitive. (except the id part)
For ex: send request to any of following uri and it still returns valid result
But if you try with case insensitive ID it will not work. for ex.
PS: for this simple test i used workbench but you can use any client and it should work