Do I need to ANALYZE table after DROP INDEX?
No, it's not necessary. Statistics on the main table are not affected by indexes at all.
One thing to observe: expression indexes introduce new &quot;derived&quot; columns, and Postgres gathers separate statistics for those. Removing such indexes also removes the special statistics - which may lead to different query plans, beyond the fact that the index is gone.
Since you mention indexes on boolean columns: those hardly ever make sense and it's a good idea to remove those. boolean column typically only make sense as condition in a partial index. There is an example in the manual.