A table actually requires a paragraph to succeed it, however this isn't really the problem with your document, what you probably have is two separate paragraphs which occurred when you split the table.
There are three methods you can use to avoid the extra paragraph at the start of the page:
Method one: Instead of splitting the table, put the cursor inside the row you want to appear on the next page and click Insert -> Page break. Word will split the table for you but will do it without creating a new paragraph
Method two: This one will work with a document where you already have a split table and an extra paragraph. Turn on formatting marks, go to the first page and click at the end of the paragraph with the page break where the paragraph end symbol is (¶). Then press Delete on your keyboard to remove the paragraph break. The extra paragraph on the start of second page should disappear.
Method Three: If you are working in Word 2003 or are in compatibility mode the first two solution won't work because Word won't split the page break and paragraph marker. Instead you can remove the "extra" paragraph on the second page by turning on formatting marks, clicking on the paragraph mark on the second page and going to Font -> Turn on Hidden. Turn off formatting marks and the extra paragraph should disappear. Just make sure not to select the whole paragraph or the page break will be hidden as well.
Method Four: Along the same lines as above, if you are working in Word 2003 or are in compatibility mode, another option is to disable the compatibility option which prevents the paragraph mark being removed while still keeping the page break. To disable this option:
- Click the Microsoft Office Button/File Tab, and then click Options.
- In the left pane, click Advanced.
In the right pane, click one of the following in the Compatibility options for list:
a. Current_document_name. Use this option if you want the changes to affect only the current document.
b. All New Documents. Use this option if you want the changes to affect all new documents.
Expand Layout Options.
- Click to deselect the Split apart page break and paragraph mark check box.