Gardaí said the tests were completed on Tuesday following Monday's crash near Westport, but the details will not be released for "operational reasons".
A spokesperson added: "Investigations are ongoing."
Police in the Republic of Ireland had issued an appeal to help find Eoghan, aged 10, Ruairi, aged 5, and their 43-year-old father Sanjeev Chada, who went missing after leaving their family home in Ballinkillen, Bagenalstown in Co Carlow on Sunday evening.
It was the first time a Child Rescue Ireland alert, designed to help locate abducted children when there is serious concern for their safety, has been issued since the system was put in place last year.
Detectives believe the boys died before the crash occurred.
Both post mortems have finished and the details will not be released for operational reasons. Investigations are ongoing.
A passer-by called 999 after spotting the vehicle, which had hit a stone wall at about 3.25pm on Monday.
Meanwhile their father is due to be interviewed by detectives.
Gardaí have appealed for anyone who may have seen him in his green Ford Focus, registration number 06 CW 238, as it travelled across the country.
Superintendent Dave Taylor said: "We are particularly interested in talking to any garage owner who may have served his car petrol, any shops, restaurants, bed and breakfasts or hotels that may have offered services to the occupants or who may have seen this vehicle."
The boys' post mortems were carried out at Mayo General Hospital on Tuesday.
It is understood toxicology tests also took place. The car was removed from the scene of the collision at Rosbeg for further technical and forensic examination.
Gardaí thanked the public who got in touch following the information appeal.
Tributes have been paid to the little boys, hailing them both as hugely popular sport fanatics.
They were members of their local hurling club in Ballinkillen, and played at under-ten and under-six level.
Local parish priest Fr Declan Foley was in the family home when the news was broken to their mother Kathleen, who is a nurse from the Carlow area.
Mass goers in the local area have been keen to show support.
Fr Declan Foley said: "The whole community has been strongly impacted by this and it was lovely last night to see the whole community gather around, and they were streaming through the house last night in huge numbers just offering their support which made such a difference."
Meanwhile the boys' school principal has paid tribute to the pair, describing them as "beautiful".
Michelle Doorley added: "This is a terrible tragedy for the Murphy and Chada families, for our school and our community and we are deeply saddened by these events, our sympathy and thoughts are with the Murphy and Chada families and all their friends.
"Eoghan was going in to fourth class and Ruairi was going into senior infants in our school and they will be greatly missed by all who knew them."