General is fine but specific is better but you have to know what exists to be specific.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.
Brady demands, in my opinion, should always be specific. For example, mine run five pages. The reason I do this is to avoid the appellate cases that state one must have specifically requested the information. I include this amount of detail in the omnibus motion following receipt of what the prosecutor supplies as a result of the initial demand to produce.
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My response is for educational purposes and does not constitute legal advice nor creates an attorney client relationship which requires all the details and a personal conference.
The purpose of the opinion in People v. Brady was to create a duty for the government to turn over to the defendant any exculpatory evidence where the government is in possession of, or aware of it, AND where the defendant is not. So, for example, if both parties are aware that a particular witness made a false identification before making a positive identification, it would not be a violation of Brady for the government to fail to advise the defendant of something he knew or should have known.
My purpose in the above example is to illustrate the fact that the defendant is not expected to ask for something, the existence of which is unknown to him or her. Further, I believe that Brady's duty applies to the government irrespective of whether any specific demand is made.
Lastly, if the potential Brady violation is so egregious to go beyond simple harmless error, and instead potentially have had an effect on the verdict, the appellate court would not be concerned about the specificity of any request.
I guess that was the long version of my answer. The short answer would be that I think a general request is more than sufficient.
The Brady Rule is often skirted by prosecutors who say, "the defense should know about this witness, it is his sister-in-law" or "we don't have to turn over parole or FBI material as we are not charged with knowing about it." The defense should list as many things as possible to put the prosecutor on notice and preserve it for appeal. I had a prosecutor withhold a photo array where the victim did not pick out the defendant. I knew the officer and asked him and he said it was in his file. The prosecutor said, "That is not exculpatory." It was the first day of trial. The judge did not even admonish him let alone punish him, but I used it to let the jury know he did something wrong and I won the case. The prosecutors do not get in trouble and neither do the police when they lie and set people up.