I believe the jurors would have been summoned personally by the coroner's officer. He would probably have used the electoral register or possibly local council records of ratepayers.
At one time jurors were selected from the electoral roll numerically - a random number was chosen and the jury picked from that; e.g. if the number was 856, then every 856th person on the roll would be called up. (I suspect it's rather more sophisticated now).
THE LISTS OF JURYMEN
Yesterday the lists of the names of those persons liable to serve as special and common jurymen in England and Wales during the year were exhibited on the doors of every church, chapel, and other public places of worship over England and Wales, where they can be inspected by every one, and where they will remain during the next two Sundays. Every person whose name appears in these lists will be liable to serve as a juryman except those who are over 60 years of age, and those among others who are exempt by reason of being peers, Members of Parliament, judges, clergymen, Roman Catholic priests, members of the bar, solicitors, officers of the Law Courts, coroners, doctors, the household servants of Her Majesty, the officers of the Post Office, Customs and Inland Revenue, Magistrates, and their staffs, and others. During the last week in this month the justices of the peace in every division in England and Wales will hold a special petty session for the purpose of correcting the lists, and of allowing any objection to serve which may be substantiated.
You're welcome. I'm not sure it shows how jurors were selected, only informed, but interesting none the less.
I did think it showed that they were selected parish by parish (I can't see them posting a list of every juror in England on every church door, they would be very long lists), but there's a puzzling bit of confusion over the Kelly inquest which seems to suggest the jurors were from two different parishes;
Daily News 13th Nov
"The jury having answered to their names, one of them said: I do not see why we should have the inquest thrown upon our shoulders, when the murder did not happen in our district, but in Whitechapel.
The Coroner's Officer (Mr. Hammond): It did not happen in Whitechapel.
The Coroner ( to the juror, severely): Do you think that we do not know what we are doing here, and that we do not know our own district ? The jury are summoned in the ordinary way, and they have no business to object. If they persist in their objection I shall know how to deal with them. Does any juror persist in objecting ?
The Juror: We are summoned for the Shoreditch district. This affair happened in Spitalfields.
The Coroner: It happened within my district.
Another Juryman: This is not my district. I come from Whitechapel, and Mr. Baxter is my coroner.
The Coroner: I am not going to discuss the subject with jurymen at all. If any juryman says he distinctly objects, let him say so. (After a pause): I may tell the jurymen that jurisdiction lies where the body lies, not where it was found, if there was doubt as to the district where the body was found.
The jury having made no further objection, they were duly sworn."
So some jurors were from Whitechapel and some from Shoreditch....