The 32-year-old star was contacted by authorities in relation to the injury Princess Tiaamii received and that her father Peter Andre discovered when she came to stay at his home.
After Pete publicly revealed the injury his daughter had sustained, Katie - who also has a five-year-old son Junior with Peter and another son, eight-year-old Harvey from a previous relationship - insisted Princess hurt herself in a "fluke accident" during a trip to Swiss ski resort Klosters with her mother and sister.
After quizzing her about the incident, police are said to be satisfied with the model-s explanation and have decided no further action will be taken.
A source close to Katie told the Daily Mirror newspaper: "She has been told by police that they are satisfied she has done nothing wrong and there will be no further action."
She is now angry that a mystery person made a "malicious" call to police about the incident, and is also furious that Peter - who was also contacted by officers about his daughter-s burn - made a call to her about the accident and filmed it for his reality TV show.
In a statement, she said: "I am deeply saddened that it would appear my ex-husband would deliberately choose to ring me and make a fuss about a minor injury to Princess and allow it to be filmed for his TV show.
"This appears to reveal his true motivation. I am not sure how this is meant to help the children, or is putting them first.
"It was clear that the intention was again to portray me as a bad mother. I admit reacting angrily to that, but of course I do not really wish any physical harm."
Meanwhile, Peter is said to be compiling a dossier against his ex-wife in a bid to gain full custody of their children Princess and Junior and asked his solicitor to make a legal application to the Family Court after Princess was burned.
The 37-year-old pop star is reportedly alleging that Katie - who is currently divorcing her second husband cage fighter Alex Reid - is an unfit mother because of her tumultuous private life.
A source told The Sun newspaper: "Peter thinks she is mentally unfit to be in charge of children. He wants full custody, even if temporary, until she sorts out her car crash of a life."