They will usually start with an interview and alibi check. If things aren’t adding up they will begin affidavits for cell phones etc.
The initial interview can be very telling. Some folks are good liars, some are not. If you are one of those people who get nervous just talking to LE even if you haven’t done anything, and there are many, and then you say you were home alone all night, you might get another look by LE.
So, an individual who seems to be forthright and honest and has a good alibi, ie in a public place with witnesses, would likely be cleared at this time. If your alibi puts you in a bar on video, that’s great, but what if upon reviewing the entire video, LE realizes that there was an extended period where the person wasn’t actually seen? LE would likely bring you back in for questioning and look for inconsistencies in your statement.
I believe there will be some difficulty corroborating alibis for people given that the crime likely took place sometime between three and four in the morning.