Should my Web Api support CORS request?

Should my Web Api support CORS request?

I am developing an application which has the following architecture.
Web Api (this web api would be consumed by three clients) (Project 1)
Web App (Client 1) (Project 2)
Mobile App (Client 2) (Project 3)
Windows App (Client 3) (Project 4)
I want to know, should my Web Api REST service has to support CORS request
so that all three clients can use the Web Api.??
Or can I create the WebApi in my WebApp project and all three clients can
access the Web Api without any problem. ??
Thanks in advance.