Single Logout using SAML authentication option

I've been able to get single sign on (SSO) working between my custom app (using Amazon Connect Streams library) and Connect, but have not found any documentation for configuring single logout (SLO). I have configured my custom application for SLO, so that when a user clicks a logout button from my app, they are logged out from the IdP and redirected back to the sign in page. The problem is, this does not log the user out of CCP. In the agent reports, they are still in the Available state (or whatever state they were in when the user logged out from my custom app).

Does Connect support SLO? Or does the user have to logout of CCP, then logout from my custom app?