The Baton Rouge Police Dept. tells TMZ Sports ... there is no probable cause to arrest LSU linebacker Jacob Phillips for rape due to "several inconsistencies" in the accuser's story.
We broke the story ... Phillips -- a highly recruited linebacker -- was investigated for sexual assault following allegations from a female LSU student athlete.
We've confirmed cops were called to a Baton Rouge hospital on June 11 to respond to the accuser -- who claims she was sexually assaulted by Phillips early that morning.
The case was investigated -- and at this point, Phillips has neither been arrested or charged with a crime.
Now, Baton Rouge PD Sgt. McKneely has issued a statement on the case ... telling TMZ Sports, "Due to several inconsistencies in the victim's narrative/disclosures and a lack of cooperation concerning evidence and further interview there was no probable cause for arrest found at this time."
We spoke with the accuser who is not backing down from the claims -- and says it's the police who aren't cooperating with her.
We also reached out to LSU for comment -- so far, no word back.