Use Powershell to query SSAS connection string
Woohoo!!! 

# Add the AMO namespace
$loadInfo = [Reflection.Assembly]::LoadWithPartialName(“Microsoft.AnalysisServices”)

## Connect and get the edition of the local server
$connection = “localhost”
$server = New-Object Microsoft.AnalysisServices.Server
$server.connect($connection)

foreach ($d in $server.Databases )
{   

    Write-Output ( “Database: {0}, String {1}:” -f $d.Name, $d.DataSources.ConnectionString)        

} # Databases


returns: 

Database: EnvironmentalAnalysisService, String Provider=SQLNCLI11.1;Data Source=LAP123;Integrated Security=SSPI;Initial Catalog=EnvironmentalDataMart:
Database: PerformanceAnalysisService, String Provider=SQLNCLI11.1;Data Source=DEV-EDW;Integrated Security=SSPI;Initial Catalog=PerformanceDataMart:

PS SQLSERVER:\SQLAS&gt;