The number of new confirmed cases in Dutchess County on this day was 9 - that is much lower than it has been. Though testing kits processed on this day was also down by half, the percentage of people testing positive of those tested is down for this day. The number of hospitalizations remains at 56 in the Dutchess County Tracker, which has been the number for a few days.

Additionally, Putnam County’s numbers have not been updated in 3 days for their own county tracker. That county was updating by posting a new PDF daily. May 15th was the last day of their daily numbers. The Putnam County Executive MaryEllen Odell stated in an advertisement that she and the Legislature was ready for the reopening, but the Philipstown Supervisor Richard Shea said that he was not, as reported in the Highlands Current. The advertisement was placed in official county newspapers such as the Putnam County News & Recorder.

UPDATE: Putnam County published their May 18, 2020 numbers.

Sources:
New York State Tracker
Dutchess County Tracker
Orange County Tracker
New York State Fatalities Tracker
Testing is limited, which implies that people testing positive for COVID-19 is not total, as many people are not tested.

DUTCHESS COUNTY 5/17/2020

How Many People Tested In Dutchess County:
22,223 (two days ago 21,395 via New York State Tracker)
How Many People Tested POSITIVE As Of This Day:
3,552 (two days ago, 3,527, via New York State Tracker)
How Many People Tested This Day:
337 (two days ago 627, via New York State Tracker)
How Many People Tested POSITIVE This Day:
9 (two days ago 29, via New York State Tracker)
Number Of People Hospitalized For COVID-19 As Of This Day:
56 (two days ago 56, via Dutchess County Tracker)
How Many COVID-19 Related Deaths As Of This Day:
124 (two days ago 117, via Dutchess County Tracker)

BEACON
Active COVID-19 Cases In Beacon On This Day:
125 (two days ago 130, via Dutchess County Tracker)

FISHKILL
Active COVID-19 Cases In Fishkill On This Day:
122 (two days ago 133, via Dutchess County Tracker)
Active COVID-19 Cases In East Fishkill On This Day:
104 (two days ago 113, via Dutchess County Tracker)

WAPPINGERS
Active COVID-19 Cases In Town of Wappingers On This Day:
98 (two days ago 104, via Dutchess County Tracker)
Active COVID-19 Cases In Wappingers Falls Village On This Day:
31 (two days ago 33, via Dutchess County Tracker)

POUGHKEEPSIE
Active COVID-19 Cases In Poughkeepsie On This Day:
185 (two days ago 196, via Dutchess County Tracker)

Active COVID-19 Cases In Poughkeepsie City On This Day:
255 (two days ago 275, via Dutchess County Tracker)

ORANGE COUNTY 5/17/2020

How Many People Tested In Orange County:
39,386 (two days ago 38,357, via New York State Tracker)
How Many People Tested POSITIVE In Total:
9,965 (two days ago 9,878, via New York State Tracker)
How Many People Tested On This Day:
367 (two days ago 715, via New York State Tracker)
How Many People Tested POSITIVE On This Day:
22 (two days ago 54, via New York State Tracker)
Number Of People Hospitalized For COVID-19 As Of This Day:
96 (two days ago 106) (via Orange County Tracker)
How Many COVID-19 Related Deaths As Of This Day:
419 (two days ago 408, via Orange County Tracker)

NEWBURGH
Active COVID-19 Cases In Newburgh On This Day:
687 (two days ago 645, via Orange County Tracker)
Active COVID-19 Cases In City of Newburgh On This Day:
1,397 (two days ago 1,314, via Orange County Tracker)

PUTNAM COUNTY 5/17/2020

How Many People Tested In Putnam County:
6,572 (last week 6.325, via New York State Tracker)
How Many People Tested POSITIVE As Of This Day:
1,141 (last week 1,127, via New York State Tracker)
How Many People Tested On This Day:
116 (last week 153, via New York State Tracker)
How Many People Tested POSITIVE On This Day:
5 (last week 6, via New York State Tracker)
How Many Active Cases In Putnam County On This Day:
33
Number Of People Hospitalized For COVID-19 As Of This Day:
10 (last week 10, via Orange County Tracker)
How Many COVID-19 Related Deaths As Of This Day:
56

PHILIPSTOWN
Confirmed COVID-19 Cases In Total In Philipstown As Of This Day:
NA (last week 113, via Putnam County Tracker)
Putnam doesn’t seem to publish an “Active Cases” per city/town/village number like Dutchess and Orange do. “Active Cases” can fluctuate up or down. “Confirmed Cases” only go up, as they are cumulative.