Always note that state law may be more restrictive on police power than the U.S. Constitution.
There are two areas of liability at issue: Federal constitutional liability and State law liability.
If the shooting is constitutionally reasonable under the 4th Amendment (i.e.: justified) then there would be no liability, even if the officer failed to qualify.
However, if the shooting was unreasonable under the 4th Amendment, then liability could exist. Under City of Canton v. Harrisi, the inadequacy of police training may serve as the basis for 42 U.S.C.S. § 1983 liability only where the failure to train amounts to deliberate indifference to the rights of persons with whom the police come into contact. Thus, if the department had a training program that was deliberately indifferent to a known training deficiency, and the training deficiency is the cause of the violation then there can be liability. In deliberate indifference for inadequate training, the Supreme Court stated the following:
The issue in a case like this one, however, is whether that training program is adequate; and if it is not, the question becomes whether such inadequate training can justifiably be said to represent "city policy." It may seem contrary to common sense to assert that a municipality will actually have a policy of not taking reasonable steps to train its employees. But it may happen that in light of the duties assigned to specific officers or employees the need for more or different training is so obvious, and the inadequacy so likely to result in the violation of constitutional rights, that the policymakers of the city can reasonably be said to have been deliberately indifferent to the need. In that event, the failure to provide proper training may fairly be said to represent a policy for which the city is responsible, and for which the city may be held liable if it actually causes injury.ii
However, the plaintiff would need to show that the failure to shoot a particular numerical score was the cause of the unreasonable shooting. This may be hard to show if the qualification course is purely test of accuracy. However, if the qualification includes a measure of decision making, then this would be easier to show.
If the officer accidentally shot an innocent third party, then failure to shoot a particular score for accuracy would have a bearing upon the constitutional violation, which would be a 14th Amendment Due Process claim rather than a 4th Amendment unreasonable force claim.
State Law Liability
The second area of liability rests in specific state law, such as negligent retention, negligent entrustment, negligent training and/or negligent supervision. Again, elements of any negligence claim are (1) the defendant owes a duty to the plaintiff, such as the duty not to put unqualified officers on the street, (2) the defendant breached the duty, such as placed an unqualified officer on the street, (3) there was an injury, such as an improper shooting, and (4) the breach of the duty was the cause of the injury. This is a summary of general negligence law; specific causes of action in a particular state would be determined by a specific state law.
In conclusion, although defenses, such as a lack of causation, may exist in the question presented, the best practice, by far, is not to place officers who have not qualified with their firearm on the street in a full duty (armed) capacity. These officers should be placed on administrative leave or held for remedial training pending qualification.