Currently there isn't any way to get or print object reference counts programmatically.
In case it is helpful, e.g. for development leak monitoring, you can get a total object count from RunGarbageCollector().
Note that if you stop or break into the BrightScript debugger, there are some commands to get information. 'var' shows local variables including ref count, 'bsc' shows an anonymous listing of objects including ref count, and 'bscs' (on firmware 6.1 or later) shows a summary of object counts by type.