A police marksman who shot dead an unarmed man will not face charges, prosecutors announced on Thursday, prompting fury from the dead man's family, who said the decision showed there was "no justice in this country".

Anthony Grainger, 36, was shot through the chest as he sat in a car in the village of Culcheth, Cheshire, on the evening of 3 March 2012.

The decision not to charge the officer came after the director of public prosecutions decided a jury would believe the police marksman's claim to have acted in self defence.

A solicitor for the Grainger family said prosecutors risked giving armed police who kill unarmed suspects immunity from criminal charges.

Sir Peter Fahy, chief constable of Greater Manchester police. Photograph: Anna Gowthorpe/PA

The Crown Prosecution Service said a charge would be brought against the chief constable of Greater Manchester police, Sir Peter Fahy, under health and safety legislation, because poor police planning had exposed Grainger and other suspects to unnecessary danger.

Fahy will be named in the charge because he is chief constable. He is not facing criminal allegations personally, has no need to attend court, and, if the jury convicts, he will not get a criminal record.

Wes Ahmed, Grainger's cousin, said: "This decision has ripped us to pieces. We thought it was a clear-cut case. When it comes to a death in custody the system protects the police. This is not justice. There is no justice in this country."

The shooting happened as Grainger was sitting in the Audi in Culcheth. The officer fired through the car's front window, and police threw a CS gas canister into the vehicle. They shot out its tyres in an operation that caused onlookers to scream in terror. No firearms were found in the car, on Grainger, nor at any address linked to him.

Jonathan Bridge, solicitor for the Grainger family, said if police were convicted for the health and safety breach, for which they would be fined, it would "just move money from one government department to another".

Bridge said the Grainger case was different from other recent cases where armed police were not charged. He said that Grainger had no history of involvement with firearms nor was there anything to suggest he would have access to them.

If correct that is in contrast to the case of Mark Duggan, 29, whom armed police correctly believed had collected a weapon minutes before they stopped a vehicle he was travelling in during August 2011.

Last week an inquest jury found that Duggan was unarmed when police shot him, having thrown the gun away seconds beforehand. The killing was ruled lawful.

In the case of Azelle Rodney, 24, shot dead in Edgware, London, in 2005, an inquiry last year found he had been unlawfully killed by an armed officer. Police had had intelligence he could have access to a machine gun. Weapons were found inside a vehicle he was riding in on the way to allegedly rob a Colombian drugs gang.

The CPS has used health and safety laws before to prosecute police for the shooting of an unarmed man, while deciding not to charge officers who pulled the trigger.

In 2007 the Met was convicted for the shooting of Jean Charles de Menezes, whom officers had mistaken for a suicide bomber. The force was fined £175,000 and ordered to pay £385,000 in costs.

In 2010 Grainger was a defendant in a multimillion-pound drugs trial and was acquitted of conspiracy to supply drugs but admitted handling stolen cars and was jailed for 20 months. His occupation is officially listed as "odd job man".

The CPS decisions were taken after Alison Saunders, the director of public prosecutions, reviewed the case.

Explaining the decision not to charge the armed officer, the CPS said: "Any prosecution for murder would require the CPS, amongst other elements, to prove beyond reasonable doubt that (a) the officer did not honestly believe it was necessary to use force and (b) that the force used was disproportionate in the circumstances as the officer believed them to be.

"In the circumstances of this case, our assessment of the evidence is that a jury would accept the officer did believe his actions were necessary and that the level of force used in response to the threat as he perceived it to be was proportionate."

Fahy, who technically faces the health and safety prosecution, must decide whether to fight the case or, after studying the evidence, plead guilty to minimise costs and damage to the force.

The first hearing in the health and safety case against Greater Manchester police will be on 10 February 2014 before Westminster magistrates.