1:09 PM PT -- Crawford's attorney Rusty Hardin ... "It's not unexpected that people are going to seek compensation when a tragic accident occurs."
"Carl was not at the pool when it happened. He was upstairs in his house. A couple of other adults were out at the patio watching the children. Little boy went down the slide and was in distress -- lady jumped in to help and she tragically drowned as well."
"Carl has made it clear to everyone how horrible he feels about this tragic accident. He deeply regrets that someone is trying to seek money for what is a tragic accident."
The mother of 1 of the drowning victims at Carl Crawford's Texas mansion last month says the former MLB star is responsible for her son's death ... and now, she's suing for over $1 million.
It's all spelled out in new court docs obtained by TMZ Sports ... in which Liban Hersi claims 38-year-old Crawford didn't do enough to prevent tragedy from striking on May 16.
In the docs, Hersi says her 5-year-old son was visiting Crawford with a family friend for a party at the former L.A. Dodgers outfielder's mansion in Harris County, Texas.
Hersi claims Crawford has a massive pool on the property ... but says it has no fencing around it -- and adds Crawford didn't take steps to protect her child from getting into the pool.
Hersi says her son fell in ... and when another partygoer jumped in after him -- they both tragically died.
Hersi claims Crawford could have done MUCH more to prevent the double drowning ... saying he had no alarm system set up for the pool and claimed the swimming hole's design was "unreasonably dangerous."
Hersi is now suing for wrongful death -- asking for over $1 million in damages.
Crawford spoke about the incident days after ... writing in a statement on social media, "My Hearts Heavy. The tragic events that occurred at my home will be with me forever. I'm at a loss for words I've struggled all week to manage my emotions and I keep thinking of the families of those who've passed and their grief, I know they have it the hardest."
He continued, "They are the first and last thing I think of these days. Please keep them in your prayers, I know they will always be in mine."
We've reached out to Crawford's reps for comment on the new lawsuit ... but, so far, no word back yet.