The Royal United Hospitals Bath NHS Foundation Trust (RUH) may have perverted the course of justice, coroner Maria Voisin heard.
It emerged lawyers for the trust had removed crucial evidence from a witness statement.
Benjamin King, son of British actor Jamie King, died on 10 May at the RUH.
The hospital has offered its condolences to Benjamin's family.
Ms Voisin, the coroner for Avon, said "the realisation that factual evidence had been removed by a solicitor" was a "very serious matter indeed".
The inquest into the death of Benjamin is now due to resume early next year.
Benjamin was born - by emergency caesarean section - on the 5 May at the RUH.
He died five days later from severe brain damage having been starved of oxygen, it's thought shortly before his birth.
His mother Tamara Podemski, a Canadian actress, had been due to have a caesarean procedure at the hospital the previous day but it had been postponed.
An investigation into the incident, found that postponing the operation was the incorrect decision.
Speaking shortly after the inquest adjournment, Mr King said: "In his short life our son Benjamin has had a profound effect on our family.
"He's taught us the true meaning of love, he asked us to be most courageous, resilient and forgiving versions of ourselves."
He added the family was "horrified" to hear a statement had been altered and the delay to the inquest was "significantly prolonging" the family's suffering.
In a statement Helen Blanchard, director of nursing and midwifery for the RUH, offered her "sympathy and condolences" to Benjamin's family.
"We regret the delay in this extremely distressing process," she said.
"We respect the Coroner's decision to adjourn the inquest and will cooperate fully with her directions.
"We are unable to comment further while proceedings continue."
The inquest is now expected to take place on 16 January.
A coroner has unexpectedly adjourned an inquest into the death of a baby and is considering whether to call for a criminal investigation.