There's no connection string for the UniSession class. Instead use the static OpenSession method of the UniObjects class.
UniSession us1 = UniObjects.OpenSession(“DENVER\\asmith”, ”username”, ”password”, “databaseAccount”, ”UDCS”);
Login=lpn;user=myUsername;password=myPassword;
Login=lpn;ConfigDBLocation=d:\folderWithConfigFolder;user=myUsername;password=myPassword;
Server=spn;Account=apn;user=myUsername;password=myPassword;
DATA SOURCE=myDataSource;LOCATION=myLocation;USER ID=myUsername;PASSWORD=myPassword;
Provider=any oledb provider's name;OledbKey1=someValue;OledbKey2=someValue;
The last parameter, UDCS, is what tells the object to connect to UniData (not UniVerse).