There is an etiquette of placing knife and fork on a plate while resting or after finishing. For example this cheat-sheet (there are a lot of texts and images like this on the web) 

I found this tradition mentioned in a 1858 year book:

On another occasion she refused to be introduced to a gentleman because at a dinner party in handing his plate to a waiter he had laid his knife and fork straight, instead of crossed, upon it; and after concluding the meal, instead of placing his knife and fork in parallel lines beside his plate, he had been so vulgar as to leave both knife and fork crossed upon his plate.

So I assume it is an old tradition. What are its origins? Are there any written sources of it?

There is evidence that an opposite etiquette prevailed in the 1840-1900 time period.

Night and Morning (1841, UK):

she crossed her knife and fork, and pushed away her plate, in token that she had done supper

"Female Education" in The Popular Educator (1856, UK):

When she has finished her dinner, say of meat and potatoes, she lays her knife and fork. close together, obliquely across the plate

Martine's Hand-book of Etiquette: And Guide to True Politeness (1866, US):

after you have finished your dinner, cross the knife and fork on the plate, that the servant may take all away

Good Manners: A Manual of Etiquette in Good Society (1870, US):

after you have finished your dinner, cross the knife and fork on the plate, that the servant may take all away

The Gentlemen's Book of Etiquette, and Manual of Politeness (1874, US):

after you have finished your dinner, cross the knife and fork on the plate, that the servant may take all away

Manners, Culture and Dress of the Best American Society (1891, US):

Do not cross your knife and fork upon your plate until you have finished.

In any case, the OP etiquette was not at all universal in the 1840-1900 period and many sources describe the opposite tradition.

An early mention of the objection to crossing the knife and fork is in the 8 March 1711 Spectator volume 1, number 7.

I dispatched my Dinner as soon as I could, with my usual Taciturnity; when, to my utter Confusion, the Lady seeing me quitting my Knife and Fork, and laying them across one another upon my Plate, desired me that I would humour her so far as to take them out of that Figure, and place them side by side. What the Absurdity was which I had committed I did not know, but I suppose there was some traditionary Superstition in it; and therefore, in obedience to the Lady of the House, I disposed of my Knife and Fork in two parallel Lines, which is the figure I shall always lay them in for the future, though I do not know any Reason for it.