<< I thought this was working - but NOT YET 
!! >> The results are very inconsistent, to the point where a space in the connection name can cause a problem.
I have older connections which resolve OK, but later one's don't. If you have correct results, please let me know.
Listing all Webi reports used by an OLAP connection as there is no Relationship query, is something I have been putting off for a while and I am still trying to work out / finalise. There are still a lot of "LIKE" clauses and not the actual full string.
The tool to use is the query builder:
http://<servername>:8080/AdminTools/querybuilder/ie.jsp
Use the query:
Select
SI_ID, SI_NAME, SI_KIND, SI_OWNER
From
CI_APPOBJECTS, CI_INFOOBJECTS
Where
SI_KIND='Webi' AND
PARENTS("SI_NAME LIKE '%Connection%'",
"CHILDREN('SI_NAME LIKE ''CommonConnection-%'' ','SI_NAME=''Vendor Balances'' ')")
The SI_NAME marked in bold is the name of your OLAP connection (case sensitive). In my case that is "Vendor Balances".
If you have any further information to replace the LIKE clauses with exact strings, please post below this blog.
Other references:
BusinessObjects Enterprise SDK - Relationship Queries