In various dictionaries, the word "市立" has "しりつ" listed as the main reading. However, they then go on to list the reading "いちりつ", with a note saying "when spoken to avoid confusion with 私立【しりつ】". This makes sense, as having the same pronunciation for two words that are completely opposite to each other would be... confusing, to say the least.
But in that case, when is しりつ actually used for 市立? If people pronounce it いちりつ "when spoken", is there at all a case where しりつ is used? And why is it listed as the main reading in dictionaries?