Telford MP Lucy Allan said she has been briefed by the Independent Police Complaints Commission association's commissioner Guido Liguori following the death of the 48-year-old on Monday.
Mr Atkinson died after being struck by a police taser outside his father's house in the Trench area of Telford.
Two West Mercia Police officers have been served with gross misconduct charges and are under criminal investigation following the incident.
Mr Liguori has also met with Mr Atkinson's family and said he estimated that the investigation would take about nine months.
Ms Allan said: "This is a tragic case and my sympathies go out to Mr Atkinson's family and friends at this terrible time.
"The IPCC will be conducting a thorough investigation and it would be wrong to speculate on this specific case until the investigation is complete.
"It is essential that the legal process is respected and given the time and resources needed to reach a conclusive position.
"Clearly, the investigation will want to consider whether the circumstances justified the level of force used, whether procedures were followed and whether the officers had been adequately trained as well as and many other relevant issues.
"The seriousness of this case cannot be understated."
Her comments come as Mr Atkinson's family said they welcomed news of a criminal investigation into two police officers following the footballer's death in Trench.
Relatives said Mr Atkinson was "not in his right mind", was suffering a number of health issues and had a weak heart.
He went into cardiac arrest in an ambulance on his way to hospital and later died.
Meanwhile, players from Real Sociedad, who Mr Atkinson used to play for, will wear black armbands in a match against Real Madrid tomorrow.