There will be negligible dimensional change due to moisture content change at that thickness. The wood will have been dried to 7% MC ±2% in the US, the target MC for kiln dried wood in North America, and the chances are that, after some moisture regain since drying, the wood will be somewhere in the 9 - 12% MC range when you buy it. You'll need to buy rough sawn 1-1/2" stuff to machine it to the thickness you're aiming for, allowing for at least 6 mm of thickness loss during initial machining to square. You might just about be able to get 27 mm out of 1-1/4" (32 mm) thick stock if you can find it, but to be sure you should buy 1-1/2" thick stuff.
Here's a bit more information for future reference. With shrinkage factors for yellow-poplar (tulipwood) of 8.2% tangentially and 4.6% radially in the MC range of 0% - 30% you can expect a 100 mm wide tangentially sawn board to change in size in service by about 1 mm for every 4 percentage points change in MC, say between 8% and 12 % MC (a fairly typical MC range in a residential kitchen). A radially sawn board, similarly 100 mm wide is likely to change in dimension by about 0.6 mm over the same moisture content range. However, you can virtually discount dealing with radially sawn poplar because the American sawmills, cutting for the commercial market, always convert sawlogs to boards using the crown cut method, thus pretty much every board will be tangentially sawn, with maybe a bit of rift sawn wood towards one or both the outer edges of a board. Slainte.
