Courier.

In 1935 a New York hospital would have most probably have used typewriters from US companies such as Underwood, Remington, Smith Premier etc.
At the scale of your image I can't tell you the make or model used.

Details of typefaces used by these and other companies changed over the years. Some key letters to check are _4_, whether open or closed -- your sample is closed and _3_ -- whether round top or flat top -- your sample is flat top. Also whether the _g_ is one story, i.e. with a tail like a hook or two story, i.e. with a closed bowl at the bottom, like a pair of glasses -- your sample is two story. There are other features of your sample that you could seek to duplicate, like the ball at the end of the tail at the top of _6_, but most people would not notice this.

If you want to duplicate the feel of a typewriter you need a monospaced font. If the font does not say then check the sample text _NMW_ or _nmw_. The _M_ and _W_ should look squeezed so that the type key width is the same as _N_. All keys are the same width, so in a monospace typewriter font the _I_ and _i_ usually have very wide serifs to fill the space.

Some monospace fonts that would work as substitutes:
LTC Remington Typewriter, [no obvious discrepancies, a fairly high probability that this was the make used, & very cleanly engineered font] http://www.myfonts.com/fonts/lanston/ltc-remington-typewriter/ Includes an italic designed by Frederic Goudy in 1927.
Remington Elite [wrong _3_, but a fairly high probability that this was the make used, & very cleanly engineered font]
http://www.myfonts.com/fonts/intellecta/remington-elite-typewriter/
Underwood Typewriter [no obvious discrepancies, a fairly high probability that this was the make used, & very cleanly engineered font]
http://www.myfonts.com/fonts/intellecta/underwood-typewriter/ also http://www.myfonts.com/fonts/t26/underwood-typewriter/
Smith Premier NF [no obvious discrepancies & very cleanly engineered font]
Intellecta Typewriter [no obvious discrepancies]
http://www.myfonts.com/fonts/intellecta/intellecta-typewriter/
Bulletin Typewriter [no obvious discrepancies]
http://www.myfonts.com/fonts/itfmecanorma/bulletin-typewriter/

If you do not need a monospace font a good generic substitute is ITC American Typewriter https://www.myfonts.com/fonts/adobe/itc-american-typewriter/

I did not include grunge or distressed faces. IMHO they are a waste of time for recreating documents.

Update:
Deleted possibly controversial comment.

Update:
I don't know if these otf fonts can be used on a Mac. If not there is always Courier,despite the one story _g_.
Don

R.I.P. Frank Spano.

I did mention Courier as an answer to "what font would be the most similar to this font that is available to mac".
Assuming that, in this case, as a prop, monospacing and colour (so, no Courier New) is more important that letter shape.
Otherwise, the already mentioned by Don American Typewriter also comes with every installation of Mac OS X.

Don't be snarky, Don! ;-)
Bardia asked the same two questions in another thread. There there was a single answer to both. Here you thoroughly answered (as usual) to the first and I tersely answered to the second.

Don, I think it is a prop. No sig for the M.D. examiner...

Copy of a blank hospital form itself is probably ligit. Text easy to set in Ps ...faking an M.D.'s signature tho seems to push the prop a little bit further than they were willing to go.