Some understanding of DNA evidence is necessary. Each typical human has 23 pairs of chromosomes, each of which can be conceived of in essence as a giant lengthy molecule of the polymer DNA. (This is not strictly right, but bear with me).
At points on the DNA which are capable of being identified by technical means are the equivalent of addresses (known as loci) where genes (shorter subsequences on the longer molecule) can be found. DNA analysis is not conducted on the whole genome, for forensic purposes. Rather, a number of loci are identified which fit specific criteria. The current standard number is 16, IIRC.
The basic criteria are:
First, they are non-coding sections, so that they are not subject to evolutionary pressure. One benefit of this is that there is wider variation found at the locus, meaning greater discrimination power. Another benefit is that risk of covariation among different loci is reduced (more about this later).
Second, they are characterised by “Short Tandem Repeats”, which means that at that particular locus, a simple unit of DNA (say, the series AGG) is repeated multiple times, the number of different multiples actually found in practice varying according to the contingent naturer of our species’ biological history. For example, analysis may show that the only variants that exist are 3, 5, 9, 11, and 15 units long. Each person has two different versions of our example gene, one from each parent. Thus, when the analysis is done, a person will typically have two different expressions of the gene from the list of possibles, for example, they might have inherited a gene with 3 repeating units on one chromosome from Mum and 11 repeating units from the paired chromosome from Dad at the same locus. Such a person is called a 3, 11 at that locus. This process is simultaneously done at 15 other loci, at each of which it will be possible to find another pair of STR numbers, such as 4,9 or whatever (each locus has a different range of possible numbers of repeats).
Assembling all 16 pairs of numbers then provides a profile for an individual. Population studies are then conducted to see how often the pairing of 3,11 appears at our first example locus. It might occur in 10% of the population. One then moves to the the second example, to see how frequently 4,9 appears, which might be in 9% of the population. The various loci are independent statistically, or near as dammit -they were chosen that way. That is the value of the lack of covariation I referred to above. As a result, one can apply the multiplication rule across all 16 loci, which typically results in a determination that the chance of the same profile appearing in another unrelated person is one in bazillions.
There are some complications in all this, and parental tests are slightly different, but this is sufficient for present purposes.
You can see that it is entirely possible for the DNA of a suspect and the DNA from a crime scene in principle to be analysed by completely different labs. And it is relatively easy to reduce a profile to a series of computer entries and load any number of profiles into a database to allow cold comparisons to be done. And indeed, this is done at a level that allows comparisons from different labs across the country and internationally.
In practice, a cold hit is rechecked by referring back to the original reference samples very carefully, but the answer to your question is that DNA profiles are computerised, and comparisons are done by computer all the time, subject to close checking.