The short answer is that historians are happy to use either inductive or abductive reasoning, as appropriate to the task in hand. I don't suppose they would hesitate to use deductive reasoning, either, if that would be helpful in a specific situation. History is a messy and complicated business.
One complication is that there are two different interpretations of what "data" means in the context of history. In one sense, "data" means the traces of the past that we find in the present. There several different kinds of data that are available. (See the first paragraph of the quotation below). From these, we can establish, in more or less detail, what happened and when and what contemporaries thought about it. This then becomes information to be interpreted so that an account that makes sense to us now can be developed - and interpretation is an approach that does not readily fall under any of the kinds of reasoning usually recognized in philosophy. But it is not, IMO, irrational.
The most helpful approach is to look at what historians say about history. For example, here's an extract from Wikipedia - History:-
"History" is an umbrella term comprising past events as well as the memory, discovery, collection, organization, presentation, and interpretation of these events. Historians seek knowledge of the past using historical sources such as written documents, oral accounts, art and material artifacts, and ecological markers. History is incomplete and still has debatable mysteries.
History is an academic discipline which uses a narrative to describe, examine, question, and analyze past events, and investigate their patterns of cause and effect. Historians debate which narrative best explains an event, as well as the significance of different causes and effects. Historians debate the nature of history as an end in itself, and its usefulness in giving perspective on the problems of the present.
Note that the key result of historical enquiry is a narrative, which is quite unlike a scientific theory. A narrative deals with specific events and does not attempt to generalize. Generalization is the heart of a scientific theory.
Note that "cause and effect" here does not necessarily have the same meaning as it does in science, because we are (mostly) dealing with the actions of people, rather than the reactions of things.
You will find a range of different views about history at:- History Today website
The study of how history has been written in the past and, indeed, in the present, is called Historiography. See Wikipedia - Historiography
Added comment on the idea of laws of history
The very idea that history produces laws comparable to scientific laws is highly contested. See, for example, Wikipedia - Historicism The truth, I think, is neatly captured by the well-known saying that history does not repeat itself, but it does rhyme. (This is often attributed to Mark Twain. This link to quoteinvestigator has more details.)