An independent inquiry has been launched after a museum curator tweeted about substances that could be used to damage statues.
Madeline Odent, of Royston Museum, Hertfordshire, mentioned substances that would render bronzes "extremely difficult" to fix.
The tweets came amid calls for statues of slave traders to be removed as part of the Black Lives Matter campaign.
The town council said it had instigated an external independent inquiry.
In a series of tweets from her "very, very personal account" earlier this week, Ms Odent said it would be an "absolute shame" if "certain household items" were thrown at statues because they would cause "irreversible bronze disease".
When someone suggested she was "offering an instruction manual" on how to damage statues, she responded: "No, I'm pretty sure I'm telling people how to avoid damaging precious and extremely valuable relics of history, without which we would immediately forget about the entirety of the British Empire".
Hertfordshire Police said officers had issued "strong words of advice... with regards to the content of the tweets".
'Deplores criminal acts'
The curator's personal Twitter account has since been deleted.
The town council, which runs the museum and employs Ms Odent, issued a statement saying it "deplores and condemns all criminal acts including damage to statues and monuments, and incitement to commit unlawful acts".
"The council has instigated an external independent inquiry into the recent use of social media by one of its employees," it said.
"This will ensure that the process is completed free from any political influence and should provide a fair and measured conclusion."
The statement said while staff were free to express their own views on private social media accounts, "this does not mean that we endorse or agree with those views".