The police officer also shot himself to death after the murder.
The murdered woman was believed to be the mistress of the police officer.
An eye-witness told the News Agency of Nigeria (NAN) that upon arrival at the school with her child, the police officer accosted the murdered woman, had some discussions with her before shooting her twice.
He added that the police officer immediately shot himself to death also.
Another eye-witness who saw the incident from a nearby building confirmed the report.
A man, claiming to be a property owner, said the police officer and the woman hired an apartment from him some weeks back and had been behaving like love birds until they started having problems five days earlier.
“They have been having issues since five days ago. When they rented the house, we were always happy with the way they showed love to each other.
“Some say the police officer was a friend of the woman, but they had been quarrelling for the past few days now,’’ the man said.
Police spokesman in Kwara, SP Ajayi Okasanmi, confirmed that a police officer killed a woman and himself on Thursday in Ilorin.
He told NAN that while details were still sketchy, he was told that it was a case of a love affair gone sour.
Okasanmi said the police had begun an investigation into the matter. (NAN)