User assigned managed identity with azure function - is it possible?

I was able set up System assigned managed identity for function that listens service bus: I turned on System Assigned identity in my function, changed connection string to 'Endpoint=my_endpoint;Authentication=ManagedIdentity' and assigned a role for function to use service bus. My function code snippet is as follows:

[FunctionName("MyAwesomeFunction")]
        public static async Task RunAsync([ServiceBusTrigger("myawesome-queue", Connection = "MyAwesomeConn")] string queueItem)
        {
            // func code
        }

Now I'm trying to do the same but using User assigned identity: I created managed identity, added it to function and assigned a role for it in service bus. But looks like it doesn't work - messages don't get to my queue. Any advice? Thanks.