The Connect to Database dialog will appear within OpenCities Map when encountering a DGN file containing a (non-graphic) MicroStation startup database element or containing elements with non-graphical database linkages attached.

Note: When in the Connect to Database dialog the Cancel button is selected and/or there is no successful database connection established, elements that have database linkages are restricted and cannot be modified or (fence) copied.  The following displayed within the message center are indicative of this condition:

Feature classes that include RDBMS properties will not be available for edit since database connection was cancelled.

Required startup database connection was cancelled, element with RDMBS properties not valid for tool.

The following variable can be set to disallow the inferred database connection check, preventing the condition and ceasing presentation of the resulting Connect to Database dialog:
MS_GEOXFM_DISALLOW_INFERRED_DBCONNECTION = 1

Further investigation, alternate strategies:

The presence or absence of the (non-graphical) MicroStation database element stored within the DGN, can be ascertained via the Database Verification Utility.

The Database Verification Utility can be launched multiple ways: 

Via the Ribbon Search tool: (F4) ... Verify Linkages

Note that hovering on the ribbon search result will reveal the pathway to reach the tool within all workflows, e.g. :

Drawing > Attach > Database ...
Map Database Linkages > Home > Database ...
Map Topology > Home > Database ...



Via Key-in:
MDL LOAD DBCHECK


Therein access the Check For Database Element tool:



Delete the database element by attempting to establish an invalid database connection.

e.g.
MDL LOAD DBCONMGR
DBCONMGR (ODBC/ORACLE/...)
db= 

Include a space or other invalid string after the equal sign.
After execution Unsuccessful CONNECT statement should be echoed in the Message Center. 
Next, perform Save Settings [CTRL+F].  The database element will be removed from the file.